João Henrique Andrade

João Henrique Andrade

Assistant Professor — Department of Mathematics
Instituto de Matemática e Estatística — Universidade de São Paulo
arXiv Scholar ORCID Lattes Lattes CV RG ResearchGate MR MathSciNet WoS Web of Science Genealogy

About

I am an Assistant Professor (Professor Doutor, MS-3.1) at the Department of Mathematics, IME-USP, and a permanent member of the graduate program PPGMAT.

I received my B.S. (2016) and Ph.D. (2020) in Mathematics from the Federal University of Paraíba, under the supervision of João Marcos do Ó and co-supervision of Fernando Codá Marques (Princeton). During my doctorate I spent a research period at Princeton University (2019–2020) with support from the Fulbright Commission. I held postdoctoral positions at the University of São Paulo (2021–2023) and the University of British Columbia (2022–2023), funded by FAPESP.

My research concerns qualitative properties of solutions to nonlinear elliptic equations arising in Differential Geometry — multiplicity, regularity, symmetry, bifurcation, and classification of asymptotic behavior.

Nonlinear PDEs Conformal Geometry Geometric Analysis Geometric Measure Theory

Recent News

Research

My work lies at the intersection of nonlinear analysis and differential geometry. The main research lines are outlined below.

Q-curvature and Higher-Order Conformal Geometry

Classification and asymptotic analysis of singular solutions to higher-order conformally invariant equations (GJMS/Paneitz operators), compactness phenomena, Delaunay-type metrics, and stability of Q-curvature functionals.

Fractional Yamabe Problem

Complete, conformally flat metrics with constant fractional Q-curvature on punctured spheres. Pohozaev-type invariants and rigidity results for nonlocal conformal operators.

Allen–Cahn Systems and Phase Transitions

Diffuse interface models for isoperimetric clusters, multiphasic Allen–Cahn–Hilliard systems on Riemannian manifolds, connections with minimal surfaces, and Conley index methods.

Nonlocal Equations

Singular solutions to Hartree equations, Schrödinger–Bopp–Podolsky systems, and nonlocal perimeter functionals arising in geometric measure theory.

Publications

Published & Accepted

  1. Nonhomothetic complete periodic metrics with constant scalar curvature
    (with J. S. Case, P. Piccione, J. Wei)
    Proc. Amer. Math. Soc. (2026), to appear.
    arXiv bib
  2. A general nonuniqueness result for Yamabe-type problems for conformally variational Riemannian invariants
    (with J. S. Case, P. Piccione, J. Wei)
    J. Geom. Anal. (2026), to appear.
    arXiv bib
  3. From bubbles to clusters: Multiple solutions to the Allen–Cahn system
    (with D. Corona, S. Nardulli, P. Piccione, R. Ponciano)
    J. Differential Equations 464 (2026), Paper No. 114189, 43 pp.
    DOI arXiv bib
  4. Asymptotics for positive singular solutions to subcritical sixth order equations
    (with J. Wei)
    Nonlinear Anal. 255 (2025), Paper No. 113757, 28 pp.
    DOI arXiv bib
  5. Compactness of singular solutions to the sixth order GJMS equation
    (with J. M. do Ó, J. Ratzkin, J. Wei)
    Math. Ann. 391 (2024), 4881–4909.
    DOI arXiv bib
  6. Asymptotics for singular solutions to conformally invariant fourth order systems in the punctured ball
    (with J. M. do Ó)
    J. Differential Equations 413 (2024), 190–239.
    DOI arXiv bib
  7. Constant Q-curvature metrics with Delaunay ends: the nondegenerate case
    (with R. Caju, J. M. do Ó, J. Ratzkin, A. S. Santos)
    Ann. Sc. Norm. Super. Pisa Cl. Sci. 25 (2024), no. 2, 965–1031.
    DOI arXiv bib
  8. Multiplicity of solutions to the multiphasic Allen–Cahn–Hilliard system with a small volume constraint on closed parallelizable manifolds
    (with J. Conrado, S. Nardulli, P. Piccione, R. Resende)
    J. Funct. Anal. 286 (2024), no. 7, Paper No. 110345, 61 pp.
    DOI arXiv bib
  9. Complete metrics with constant fractional higher order Q-curvature on the punctured sphere
    (with J. Wei, Z. Ye)
    J. Geom. Anal. 34 (2024), no. 1, Paper No. 6, 77 pp.
    DOI arXiv bib
  10. Some results on strongly coupled systems
    (with J. M. do Ó)
    Mat. Contemp. 54 (2023), 157–172.
    DOI bib
  11. Qualitative properties for solutions to conformally invariant fourth order critical systems
    (with J. M. do Ó)
    Discrete Contin. Dyn. Syst. 43 (2023), no. 8, 3008–3042.
    DOI arXiv bib
  12. Qualitative properties for solutions to subcritical fourth order systems
    (with J. M. do Ó)
    Nonlinearity 35 (2022), no. 10, 5249–5296.
    DOI arXiv bib
  13. Compactness within the space of complete, constant Q-curvature metrics on the sphere with isolated singularities
    (with J. M. do Ó, J. Ratzkin)
    Int. Math. Res. Not. IMRN (2022), no. 21, 17282–17302.
    DOI arXiv bib

Submitted & Preprints

  1. Quantitative stability for the Trudinger–Moser inequality (2026)
    (with J. F. de Oliveira, J. M. do Ó, A. C. Macedo, J. Ratzkin)
    arXiv bib
  2. Survey on topological methods for Allen–Cahn equations and systems (2026)
    (with S. Nardulli, R. Ponciano)
    arXiv bib
  3. Classification of fractional, singular Yamabe metrics on a twice punctured sphere I (2025)
    (with A. DelaTorre, J. M. do Ó, J. Ratzkin, J. Wei)
    arXiv bib
  4. Local asymptotics for singular solutions to critical Hartree equations (2025)
    (with T. Feng, P. Piccione, M. Yang)
    arXiv bib
  5. Quantitative stability of the total Q-curvature near minimizing metrics (2024)
    (with T. König, J. Ratzkin, J. Wei)
    arXiv bib
  6. Nonuniqueness results for constant sixth order Q-curvature metrics on spheres with higher dimensional singularities (2023)
    (with P. Piccione, J. Wei)
    arXiv bib
  7. Classification for positive singular solutions to critical sixth order equations (2022)
    (with J. Wei)
    arXiv bib

Talks & Events

Invited Talks

Seminars

Supervision

Current Students

LevelStudentFundingPeriod
PhD Angélica Ponciano CAPES-DS 2024–
MSc Bruno Gehlen — 2025–
MSc Tomas Odo — 2026–
MSc Denis Xavier — 2026–
IC Addo Del Grossi Neto FAPESP #2026/07341-8 2026–
IC Athaide Belo FAPESP #2025/22550-0 2026–
IC Bruno Hernandes FAPESP #2025/06697-0 2026–
IC Guilherme Liberato — 2026–
IC Roberto Genofre — 2026–
IC Davi Dantas — 2026–

Concluded

LevelStudentTopicPeriod
TCC Tomas Odo Trabalho de Conclusão de Curso, IME-USP 2025
IC Athaide Belo Iniciação Científica (FAPESP) 11/2024–10/2025

Grants & Awards

Active Research Grants

Completed Research Grants & Fellowships

Awards

Teaching

Courses taught at USP:

SemesterCodeCourseLevel
2026/1 MAT2453 Cálculo Diferencial e Integral I Undergrad (IF)
2025/2 MAT2454 Cálculo Diferencial e Integral II Undergrad (IF)
2025/1 MAT5711 Cálculo Avançado Graduate (IME)
2025/1 MAT2453 Cálculo Diferencial e Integral I Undergrad (IQ)
2024/2 MAT1352 Cálculo para Funções de Uma Variável Real II Undergrad (IF)
2024/1 MAT1351 Cálculo para Funções de Uma Variável Real I Undergrad (IME)

Interactive Maps

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Collaborators Around the World

Interactive map showing research collaborators and their institutions across Brazil, the Americas, Europe, and Asia.

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Academic Journey

Education, postdocs, invited talks, seminars, and events attended — from João Pessoa to Vancouver.

Contact

Address

Instituto de Matemática e Estatística

Universidade de São Paulo

Rua do Matão, 1010 — Sala A113

05508-090 São Paulo — SP, Brasil

Email

andradejh@ime.usp.br

Past: andradejh@mat.ufpb.br · jhsda@princeton.edu · andradejh@math.ubc.ca

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