
The Geometry
Seminar at IMEUSP is organized by Prof. Marcos Alexandrino and Prof. Paolo Piccione and supported by Projeto
TemáticoFapesp of Prof. Paolo Piccione ( Fapesp 2016/237466/Fapesp: 2011/213622)
SP Geometry Seminar (new!): This
is a joint seminar that is organized by the research groups of
IMECCUnicamp ( Prof. Lino Grama and Prof. Henrique Sa'
Earp), IMEUSP ( Prof. Marcos Alexandrino and Prof. Paolo
Piccione), UFABC (Prof.Francisco J. Gozzi and Prof. Marcus Marrocos), UFSCar (Prof.Luiz Hartmann and Prof. Guillermo Antonio Lobos Villagra), ICMCUSP (Prof.Fernando Manfio), Unifesp (Prof.Llohann Dallagnol Sperança)
Next talks and events:
 December, 20 2019 at 16h
 Title: Convex Algebraic Geometry of Curvature Operators
 Speaker: Prof. Renato Bettiol ( Cuny EUA)
 Abstract: I
will discuss the structure of the set of algebraic curvature operators
of ndimensional Riemannian manifolds satisfying a sectional curvature
bound (e.g., nonnegative or nonpositive sectional curvature), under the
light of the emerging field of Convex Algebraic Geometry. More
precisely, we completely determine in what dimensions n this convex
semialgebraic set is a spectrahedron or a spectrahedral shadow (these
are generalizations of polyhedra where linear programing extends to as
semidefinite programming, and are of great interest in applied
mathematics and optimization). Furthermore, if n=4, we describe this
set as an algebraic interior with respect to an explicit irreducible
polynomial.
This is based on joint work with M. Kummer (TU Berlin) and R. Mendes (Univ of Oklahoma).
 venue: 266A (IMEUSP)
Future talks and events:
Previous talks and events:
 Dezember 05, 2019 (SP Geometry Seminar at Unicamp): Prof. Llohann Dallagnol Sperança (Unifesp)
 Dezember 05, 2019 (SP Geometry Seminar at Unicamp): Prof. Alexandre Paiva(UFScar)
 Dezember 05, 2019 (SP Geometry Seminar at Unicamp): Hugo Cattarucci Botós (ICMC) short presentation
 Dezember 05, 2019 (SP Geometry Seminar at Unicamp): Jackeline Conrado (USP)short presentation
 November 29, 2019 at 14h
 Title: Produtos
torcidos com curvatura harmônica sobre superfícies"
(trabalho em colaboração com Paolo Piccione)
 Speaker: Prof. Andrzej Derdzinski (Ohiostate)
 Abstract:Uma
variedade riemanniana é dita ter curvatura harmônica
se a divergência do seu tensor de curvatura é nula
(ou,equivalentemente, o seu tensor de Ricci satisfaz à
equação de Codazzi). Nós descrevemos a estrutura
local das variedades riemannianas de dimensões $n>3\,$ que,
além de possuir curvatura harmônica, admitem
decomposições não triviais como produto
torcido com bases bidimensionais. A descrição, expressa
em termos da função torção $\phi$ e
da métrica $\,g=\phi^{\nh2}\nh h\,$ conforme á
métrica da base $h$, envolve uma dicotomia natural: ou $g$ tem
curvatura Gaussiana $K$ constante, ou $K$ é não
constante e igual a uma função específica da
função torção $\phi$. Em ambos os casos
$\phi$ satisfaz a uma equação diferencial quaselinear
elíptica da segunda ordem. Construímos também
exemplos ilustrando que ambos os casos acima são realizados por
variedades compactas.
 November 29, 2019 at 15h
 Title: Formal integrability of geometric structures
 Speaker: Francesco Cattafi (Utrecht University)
 Abstract: A Lie pseudogroup $\Gamma$ is a collection of locally defined diffeomorphisms arising as solutions of a PDE.
This object gives rise to the notion of $\Gamma$structure on a manifold $M$:
it is a maximal atlas whose changes of coordinates take values in $\Gamma$.
For instance, the set of local symplectomorphisms of the canonical symplectic structure of
$\mathbb{R}^{2n}$ forms a Lie pseudogroup, and the associated $\Gamma$structure
is a symplectic structure on $M$. More generally, any integrable $G$structure is a special kind of $\Gamma$structure.
This leads us to a natural question: what is the counterpart of a nonintegrable $G$structure in the Lie pseudogroup world
(which we call "almost $\Gamma$structure")? And when does an almost
$\Gamma$structure come from a $\Gamma$structure? In this talk we are
going to review these notions and provide an answer to the questions
sketched above. In particular, we present a new characterisation of
formal integrability in the setting of $\Gamma$structures; this
will be obtained by introducing the concept of principal Pfaffian
bundle and studying its prolongations to higher orders; we draw
inspiration from similar results for PDEs on jet bundles and for
$G$structures, which we are going to recover. This is joint work with
Marius Crainic.
 Short Lectures:
 November 26,27,28, 2019 at 14h
 Title: An introduction to Lie pseudgroups and Geometric Structures
 Speaker: Francesco Cattafi (Utrecht University)
 venue:165B (IMEUSP)
 Abstract: In this minicourse I aim to present
a general theory of geometric structures described by a Lie pseudogroup
and to study the related integrability problem.
 Lecture 1  The problem: integrability of almost structures
 Lecture 2  The tools: principal Pfaffian bundles
 Lecture 3  The solution: prolongations and intrinsic torsions
 November 22, 2019 at 15:15h
 Title: The behavior of basic equivariant cohomology of Killing foliations under deformations.
 Speaker: Dr. Francisco Caramello (IMEUSP)
 Abstract: Killing
foliations form an important class of Riemannian foliations which
includes foliations given by orbits of isometric actions and Riemannian
foliations on simply connected manifolds. Such foliations have a
builtin action of a Lie algebra of Killing vector fields whose orbits
are the closures of the leaves. It is then natural and relevant to
study the basic equivariant cohomology (with respect to this action) of
those foliations. On the other hand, we’ve obtained recently a
deformation technique for Killing foliations which allows one to reduce
many aspects of their study to the geometry and topology of orbifolds.
In this talk we will see that the ring structure of basic equivariant
cohomology is preserved throughout those deformations and, as a
consequence, coincides with equivariant cohomology of an orbifold ,
with respect to a torus action. As an application, we’ll give an
algebraic condition for the basic Betti numbers to remain constant
thoughout deformations.
 Preliminary talk of 2nd Workwhop of
the São Paulo Journal of Mathematical Science
 November 11, 2019 at 14:00h
 Title: A "promenade" towards energy an volume of unit vector fields.
 Speaker: Prof. Fabiano Brito
 Abstract:
We present results on the subject in the title. The general goal is to
tell about "interesting " minimizations of the volume and energy
functional for unit flows . Most of the subject is in relation to
previous or future papers written or to be written in collaboration
with the following co authors:P. Walczak,A. Naveira,P. Chacon,O. Gil
Medrano,V. Borrelli R. Mesquita, A. Gomes,G. Nunes , I. Gonçalves. A.
Nicoli,J. Conrado .This order is intended to be chronological
according to date of publications( or expected future ones)
 venue: 243A (IMEUSP)
 Event: 2nd Workwhop of
the São Paulo Journal of Mathematical Science: JeanLouis
Koszul in São Paulo, His Work and Legacy
 November 1314, 2019
 https://www.ime.usp.br/~2wspjm/
 SP Geometry Seminar
 November 8, 2019 at 14.00h
 Title: Existence Defects of Geometric Structures
 Speaker: Prof. Michel Nguiffo Boyom (Alexander Grothendieck Research Institute, University of Montpellier, France.)
 Abstract:
Let $S) be a type of Geometric structure. A smooth manifold $M$
is called a $S$manifold when it is equipped with a structure of type
$S$. A foliation the leaves of which are smoothly $S$manifolds is
called a foliation of type $S$, ( the notion of $S$foliation might
carry another meaning.) Given a smooth manifold $M$, let $S$ be a type
of Geometric structure. Arises the question whether $M$ can support a
foliation of type $S$. That is a rather hard problem in the
differential topology. The aim is to point out that for many important
types of Geometry structures this existence problem is linked with
sheaves of associative algebras of solutions of Hessian equations
defined by Koszul connections in the tangent bundle $TM$. The talk is
devoted to overview a few cases of geometric structures which have
significant impacts on other research domains. Instances are Hessian
structures in Riemannian manifolds; Hessian structures in locally flat
manifolds; symplectic structure in manifolds; left invariant symplectic
structure in Lie groups.
 venue: Auditório Jacy Monteiro (IMEUSP)
 SP Geometry Seminar
 November 8, 2019 at 15.00h
 Title: On the spectrum of warped products and $G$manifolds
 Speaker: Prof. Marcus Marrocos (UFABC)
 Abstract: see links
 venue: Auditório Jacy Monteiro (IMEUSP)
 SP Geometry Seminar short presentation
 November 8, 2019 at 16.30h
 Title: A semilocal model for singular Riemannian foliations.
 Speaker: Marcelo Inagaki (USP)
 Abstract: In this talk
we present a semilocal model for a singular Riemannian foliation
$\mathcal{F}$. More precisely, in a distinguish tubular neighbourhood,
the first order approximation of $F$ (linearized foliation
$\mathcal{F}^\ell$) wich partially describes the dynamic of
$\mathcal{F}$ will be given by the action of a Lie groupoid. Moreover
$\mathcal{F}$ and $\mathcal{F}^\ell$ will be foliated diffeomorphic to
a generalization of the holonomy foliation and his linearization,
respectivelly. This talk is based on joint work with prof. Marcos
Alexandrino (IMEUSP) and prof. Ivan Struchiner (IMEUSP).
 venue: Auditório Jacy Monteiro (IMEUSP)
 SP Geometry Seminar short presentation
 November 8, 2019 at 17:00h
 Title: Moduli space of contact Instantons in $7$dimensions
 Speaker: Luiz Portilla (IMECC)
 Abstract: see link
 venue: Auditório Jacy Monteiro (IMEUSP)
 October 18, 2019 at 15.15h
 Title: Cheeger deformations and Positive Ricci and Scalar curvatures
 Speaker: Leonardo F. Cavenaghi (IMEUSP)
 Abstract:
Let $(M,g)$ be a compact Riemannian manifold with an isometric
$G$action. If a principal orbit has finite fundamental group and the
quotient space has a metric with positive Ricci curvature, then Searle
and Wilhelm showed that $M$ carries a $G$invariant metric of positive
Ricci curvature. To do so, they make use of a conformal change on the
original metric and Cheeger deformations. The question remained whether
Cheeger deformations are sufficient to prove the Theorem. In this short
talk we discuss how to approach this question studying the tensors
associated to Cheeger deformations on singular points of the action. We
both construct examples where the Cheeger deformation is not enough and
give sufficient (algebraic) conditions where the deformation is enough.
Once understood the geometry near singular points, we show that
provided $G$ is nonabelian, any $G$invariant metric develops
positive scalar curvature after a finite Cheeger deformation. This is a
joint work with Renato J.M. e Silva and Llohann D. Sperança.
 October 18, 2019 at 15.40h
 Title: A topological lower bound for the energy of a unit vector field on a closed euclidean hypersurface
 Speaker: Adriana Vietmeier Nicoli (IMEUSP)
 Abstract: For a unit
vector field on a closed immersed Euclidean hypersurface $M^{2n+1}$ ,
$n ≥ 1$, we exhibit a nontrivial lower bound for its energy which
depends on the degree of the Gauss map of the immersion. When the
hypersurface is the unit sphere $S^{2n+1}$, immersed with degree
one, this lower bound corresponds to a well established value from the
literature. We introduce a list of functionals $B_k$ on a compact
Riemannian manifold $M^m$, $1 ≤ k ≤ m$, and show that, when the
underlying manifold is a closed hypersurface, these functionals possess
similar properties regarding the degree of the immersion. In addition,
we prove that Hopf flows minimize $B_n$ on $S^{2n+1} .
This is a joint work with Fabiano G. B. Brito and Ícaro Gonçalves.
 October 4, 2019 at 14h
 Title: On Mean curvature flow of Singular Riemannian foliations: Non compact cases..
 Speaker: Prof. Marcos Alexandrino (IMEUSP)
 Abstract:In this
talk we discuss the mean curvature flow (MCF) of a regular
leaf of a closed generalized isoparametric foliation as initial datum,
generalizing previous results of Radeschi and first author. We show
that, under bounded curvature conditions, any finite time
singularity is a singular leaf, and the singularity is of type I. We
also discuss the existence of basins of attraction, how cylinder
structures can affect convergence of basic MCF of immersed submanifolds
and make a few remarks on MCF of non closed leaves of
generalized isoparametric foliation.
This talk is based on a joint work with Leonardo F. Cavenaghi, Icaro Gonçalves
 September 20, 2019 at 14h
 Title: Projectively induced Ricciflat Kaehler metrics.
 Speaker: Prof. Michela Zedda
 Abstract:The first
part of this talk gives an overview of the problem of classifying
KaehlerEinstein manifolds which admit a Kaehler immersion into the
complex projective space, which leads to the conjecture that the only
Ricciflat projectively induced Kaehler metric is the flat one. In the
second part, we give evidence to this conjecture for the Calabi's
Ricciflat metrics on holomorphic line bundles over compact
KaehlerEinstein manifolds.
 venue: 259A (IME)
 August 23, 2019 at 16h
 Title: The analysis of the Ricci flow on compact manifolds
 Speaker: Adam Rudnik
 Abstract:In this talk I
will present DeTurck’s proof of the existence and uniqueness of
the Ricci flow on compact manifolds.
I will then briefly talk about a condition to the long time existence of the Ricci flow. In the last part
I will present what is known in the case of compact, orientable 2dimensional manifolds.
 venue: 268A (IME)
 August 30, 2019 at 14h
 Title: Widths and volumes of threespheres
 Speaker: Prof. Lucas Ambrozio
 Abstract:
Simon and Smith have shown that every Riemannian
threedimensional sphere contains an embedded minimal twosphere
by implementing a minmax procedure for the area functional in
the space of embedded twospheres. Such procedure actually
defines a geometric invariant as well, which we call 'width'. In
this talk, we will discuss results that compare the width to
other geometric invariants of Riemannian theespheres, e.g. the
total volume. In particular, we
prove a sharp inequality between widths and volumes that characterise
the canonical metric, and show that equidistribution of minimal
twospheres of bounded index and area is a phenomenon associated
to local maxima of the width among unit volume metrics in a given
conformal class. This is joint work with Rafael Montezuma.
 venue: 268A (IME)
 August 15, 2019 at 14h
 Title: Função Transnormal Finsleriana
 Speaker: Prof. Benigno Alves (UFBA)
 Abstract:
Nesta palestra apresentaremos o conceito e algumas propriedades de
função Transnormal Finsleriana que é uma
generalização da função distância.
Quando tal função é analítica com fibras
conexas definida em uma variedade Finsler compacta, seus níveis
são subvariedades equidistantes, em particular, constituem uma
folheação Finsleriana singular.
Por fim apresentaremos condições que garantem a
existência de uma métrica Riemanniana tal que a
função em questão é transnormal
Riemanniana. Tal apresentação é baseada em
trabalho conjunto com Prof. M. Alexandrino e Profa H. R. Dehkordi,
 venue: 101B (IME)
 August 15, 2019 at 15h
 Title: Submanifold Theory of Finsler manifolds
 Speaker: Prof. Miguel Angel Javaloyes (MurciaSpain)
 Abstract: In this talk,
we will describe basic results in the theory of submanifolds of Finsler
manifolds. First, we will give some tools needed for this study. In
particular, we will show that it is possible to define a LeviCivita
anisotropic connection associated with a Finsler metric. We will also
show how to define the derivative of an anisotropic tensor (a tensor
which depends on the direction rather than on the points of the
manifold) and how to define the curvature tensor of an anisotropic
connection, giving some results as Bianchi Identities and formulas
relating the curvature of two different anisotropic connections. Next,
we will study the curves that minimize the distance to a submanifold,
showing that locally orthogonal geodesics are minimizers and that in
fact, there exist tubular neighbourhoods of precompact submanifolds.
This result is crucial for the study of singular Finsler foliations.
Afterwards, we will study the Gauss equation of a submanifold and we
will finish the talk speaking briefly about minimal submanifolds and
the embedding problem.
 venue: 101B (IME)
 August 16, 2019 at 14h
 Title: Estimativas para o primeiro autovalor do operador Laplaciano Aproximado
 Speaker: Prof Giovanni Nunes
 Abstract: see link
 venue: 101B (IME)
 August 16, 2019 at 15h
 Title: Invariant theory for real reductive representations
 Speaker: Prof. Leonardo Biliotti (ParmaItaly)
 Abstract: Let G be
a connected real reductive Lie group acting linearly on a finite
dimensional vector space V over R. This action admits a KempfNess
function and so we have an associated gradient map. If G is Abelian we
explicitly compute the image of G orbits under the gradient map,
generalizing a result proved by Kac and Peterson in the complex
setting. We also give a new proof of the HilbertMumford
criterion and the KempfNess Theorem for real reductive Lie
groups avoiding any algebraic result. Finally we investigate the
natural G action on the projective space P(V) and we discuss some new
results wich are still in working in progress.
 venue: 101B (IME)
 USPUNICAMP Geometry Seminar 321 (IMECC).
 June 27, 2019 : 14:00  15:00
 Title: Anosov actions which are affine
 Speaker: Dr. Uirá Norberto Matos de Almeida (posdoc IMEUSP)
 Abstract: http://www.ime.unicamp.br/~geodif/index.html
 USPUNICAMP Geometry Seminar 321 (IMECC).
 June 27, 2019 : 15h15:30h
 Title: Bifurcation and Local Rigidity of Homogeneous Solutions to the Yamabe Problem on Maximal Flag Manifolds
 Speaker: Kennerson Nascimento de Sousa Lima UNICAMP
 Abstract: http://www.ime.unicamp.br/~geodif/index.html
 USPUNICAMP Geometry Seminar 321 (IMECC).
 June 27, 2019 : 15:45h16:45h,
 Title: Gap de energia em teoria de YangMills para variedades completas com invariante de Yamabe positivo
 Speaker: Prof Matheus Vieira (UFES)
 Abstract: http://www.ime.unicamp.br/~geodif/index.html
 June 28, 2019 at 14h
 Title: Lie groupoids and semilocal models of Singular Riemannian foliations
 Speaker: Marcos Alexandrino (IMEUSP)
 Abstract:
In a previous paper, Radeschi and Alexandrino, proved the
conjecture of Molino that for every singular Riemannian foliation
(M,F), the partition given by the closures of the leaves of F is again
a singular Riemannian foliation. For that they studied the linearized
subfoliation of F that roughly speaking describe the semilocal
dynamical behavior of F.
In this talk we define a Lie groupoid whose orbits are the leaves of
the linearized subfoliation and review the semilocal models of
Singular Riemannian foliations. This talk is based on a joint work
with Marcelo K. Inagaki (IMEUSP) and prof. Ivan Struchiner
(IMEUSP).
 venue: B138 (IME)
 June 19, 2019 at 14h
 Title: Ações aleatórias na Esfera de Riemann
 Speaker: Lucas Kaufmann Sacchetto (Paris 6)
 Abstract:
Os automorfismos da Esfera de Riemann são representados
por matrizes em SL_2(C), que agem por meio de
transformações de Möbius. Considere o seguinte
problema: dadas duas matrizes A e B em SL_2(C), o que podemos dizer
sobre a ação de produtos da forma …AABABBBABA onde
A e B são escolhidos aleatoriamente e o número de
matrizes tende ao infinito? Esse problema e seus variantes remontam aos
anos 60 com o trabalho pioneiro de Furstenberg. Mesmo depois de muitos
avanços realizados nos anos 70 e 80, o assunto continua a
despertar interesse até os dias de hoje e respostas definitivas
a algumas questões foram dadas apenas recentemente. O plano
dessa palestra será apresentar alguns resultados básicos
dessa teoria e mostrar como podemos olhar para o problema sob o ponto
de vista da Dinâmica Holomorfa.
 May 24, 2019 at 15h16h
 Title: Anosov actions which are affine
 Speaker: Dr Uirá Norberto Matos de Almeida (IMEUSP)
 Abstract:
There exists a standing conjecture that higher ranked abelian Anosov actions are always algebraic.
This conjecture does not hold true for generic Anosov flows, however, it is known that in the presence
of some additional geometric conditions, it is possible to show the ”algebraicity” of this flows.
Motivated by this, we proposed the study of Anosov actions with some additional geometrical conditions.
In this talk, we present some conditions under which a higher ranked abelian Anosov action is conjugated to
an affine action of $\mathbb{R}^k$ on a homogeneous space $\Gamma \backslash G \slash H$.
We put the nonspecialized public at ease and assure you that basic
concepts will be recalled and this talk is direct to the mathematical
public at large.
 USPUNICAMP Geometry Seminar (at IME USP)
 May 17, 2019 at 14h15h
 Title:
Hipersuperfícies mínimas em $S^5$ com curvatura escalar e
função simétrica elementar $\sigma_3$ constantes
 Speaker: prof. Luiz Amancio Machado de Sousa Junior
 Abstract: vide link
 venue: B4 (IME)
 USPUNICAMP Geometry Seminar (at IME USP)
 May 17, 2019 at 15h16h
 Title: ACTIONS ON POSITIVELY CURVED MANIFOLDS AND BOUNDARY IN THE ORBIT SPACE
 Speaker: prof. Claudio Gorodski (IMEUSP)
 Abstract:
We study isometric actions of compact Lie groups on
complete orientable positively curved nmanifolds whose orbit space has
nonempty boundary in the sense of Alexandrov geometry and prove that
for sufficiently large
n (in terms of the Lie group), either the group has a fixed point, or a
normal subgroup thereof, containing all isotropy groups associated to
boundary strata, has a fixed point. Among our applications, we classify
representations of simple Lie groups whose orbit space has nonempty
boundary. (joint work with A. Kollross and B. Wilking).
 venue: B4 (IME)
 USPUNICAMP Geometry Seminar (at IME USP)
 May 17, 2019 at 16:30h17h
 Title: Tduality and mirror symmetry on nilmanifolds (Short Communications)
 Speaker:Dr Leonardo Soriani (UNICAMP)
 Abstract:
opological Tduality can be undestood as a Courant algebroid
isomorphism. This allows one to transport generalized complex
structures between Tdual spaces. Sometimes this transport has a mirror
symmetric behaviour, that is,
it transports a symplectic structure to a complex one. We show that
this phenomena translates very well into a Lie algebraic setting,
yielding the notion of infinitesimal duality, Under reasonable
assumptions, infinitesimal duality of nilpotent Lie algebras can be
upgraded to actual Tduality on corresponding nilmanifolds. We also
show how this machinery is used to transport generalized complex branes
between Tduals.
 venue: B3 (IME)
 USPUNICAMP Geometry Seminar (at IME USP)
 May 17, 2019 at 170h17:30h
 Title: A topological
lower bound for the energy of a unit vector fieeld on closed Euclidean
hypersurfaces (Short Communications)
 Speaker: Adriana Nicolli (IMEUSP)
 Abstract:
see Link
 venue: B3 (IME)
 May 10, 2019 at 14h16h
 Title: Métricas maximamente torcidas de curvatura harmônica
 Speaker: Prof. Andrzej Derdzinski (The Ohio State University)
 Abstract:
Uma variedade riemanniana é dita de ter
curvatura harmônicas e a divergência do seu tensor de
curvatura é nula (ou, o que é o mesmo, o seu
tensor de Ricci satisfaz `a equação de Codazzi).
Nós descrevemos a estrutura local das variedades riemannianas de
dimensões n > 2 que, al ém de possuir curvatura
harmônica, admitem o número máximo, em um sentido
bem definido, de decomposições produto torcido locais e,
ao mesmo tempo, em algum ponto, seu tensor de Ricci tem n autovalores
distintos. Mostramos também que em cada dimensão n
> 2 fixa, os tipos de isometria local de tais variedades formam um
espaço de módulos de dimens~ao finita, e que um
subconjunto aberto não
vazio deste espaço é realizado por m étricas completas.
(trabalho em colaboração com Paolo Piccione)
 March 22, 2019 at 14h
 Title:
Critérios de solubilidade de tipo Serrin para problemas de
Dirichlet para equações de curvatura média
prédeterminada em variedades
 Speaker: Dra. Yunelsy Napoles Alvarez (Pucrio)
 Abstract:
Neste seminário apresentaremos novos resultados de
não existência e de existência de gráficos
verticais no produto MxR com curvatura média
prédeterminada H=H(x,z), onde M é uma variedade completa
de dimensão n. Como consequência de tais resultados se
derivam critérios de solubilidade sharp para o problema de
Dirichlet para a equação vertical da curvatura
média H em MxR. Esses resultados generalizam resultados
clássicos de JenkinsSerrin e de Serrin no ambiente Euclidiano,
bem como resultados de Spruck no contexto MxR.
 venue: 241A(IME)
 March 22, 2019 at 14h
 Title:
Critérios de solubilidade de tipo Serrin para problemas de
Dirichlet para equações de curvatura média
prédeterminada em variedades
 Speaker: Dra. Yunelsy Napoles Alvarez (Pucrio)
 Abstract:
Neste seminário apresentaremos novos resultados de
não existência e de existência de gráficos
verticais no produto MxR com curvatura média
prédeterminada H=H(x,z), onde M é uma variedade completa
de dimensão n. Como consequência de tais resultados se
derivam critérios de solubilidade sharp para o problema de
Dirichlet para a equação vertical da curvatura
média H em MxR. Esses resultados generalizam resultados
clássicos de JenkinsSerrin e de Serrin no ambiente Euclidiano,
bem como resultados de Spruck no contexto MxR.
 March 15, 2019 at 14h
 Title: Genuine infinitesimal bendings of Euclidean submanifolds
 Speaker: Miguel Ibieta Jiménez (IMPA)
 Abstract:
In this talk we focus on a notion of bending of a submanifold.
This notion is associated to variations of a submanifold by immersions
that preserve lengths ``up to the first order". More precisely, an
infinitesimal bending of an isometric immersion $f:M^n \to
\mathbb{R}^{n+p}$ is the variational vector field associated to
a variation of $f=f_0$ by immersions $f_t$ whose induced metrics
$g_t$ satisfy $g'_t(0)=0$. We present some results concerning
genuine infinitesimal bendings of submanifolds in low codimension. That
an infinitesimal bending is genuine means that it is not determined by
an infinitesimal bending of a submanifold of larger dimension. We show
that a strong local condition for a submanifold to be genuinely
infinitesimally bendable is to be ruled and we estimate the dimension
of the rulings. We also describe the situation for infinitesimal
bendings of compact submanifolds in codimension $2$. Finally, we give a
description of the complete Euclidean hypersurfaces that are
infinitesimally bendable.
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