Curriculum vitae
Jungang Li
Professor School of Mathematical Sciences
University of Science and Technology of China
jungangli@ustc.edu.cn Room 418, School of Mathematical Sciences, Hefei, China
Academic appointments
Professor
University of Science and Technology of China
Tamarkin Assistant Professor
Brown University · Mentor Professor Jill Pipher
Education
Ph.D. in Mathematics
University of Connecticut · Advisor Professor Guozhen Lu
Doctoral studies in Mathematics
Wayne State University · Advisor Professor Guozhen Lu
B.S. in Applied Mathematics
Zhejiang University · Advisor Professor Weimin Sheng
Research interests
- Sharp functional inequalities. Sobolev, Hardy–Sobolev–Maz’ya, Trudinger–Moser, and Adams inequalities on Riemannian and sub-Riemannian manifolds.
- Nonlinear elliptic and geometric PDEs. Variational existence, symmetry and classification, stability, and compactness for critical equations on hyperbolic spaces, product manifolds, and the Heisenberg group.
- Elliptic boundary value problems. Elliptic equations and systems in nonsmooth settings, including p-ellipticity, the Lamé system, and homogenization.
Honors and awards
- Michael Neumann Dissertation Award, University of Connecticut, 2019.
- Doctoral Dissertation Fellowship, University of Connecticut, Spring 2017.
- Outstanding Research Achievement, Department of Mathematics, Wayne State University, 2016.
Research record
Publications
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2026
Some existence results for the higher-order Brézis–Nirenberg problem on hyperbolic spaces
Advanced Nonlinear Studies, published online 17 September 2026.
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2026
Conformally invariant equations with negative critical exponents on the three dimensional hyperbolic space
Calculus of Variations and Partial Differential Equations 65 (2026), Article 248.
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2025
Symmetry of solutions to higher and fractional order semilinear equations on hyperbolic spaces
Analysis and Geometry in Metric Spaces 13 (2025), no. 1, Article 20250034.
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2025
The method of moving spheres on the hyperbolic space and the classification of solutions and the prescribed Q-curvature problem
Advances in Mathematics 482 (2025), Paper No. 110606.
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2023
Potential Characterizations of Geodesic Balls on Hyperbolic Spaces: A Moving Plane Approach
Journal of Geometric Analysis 33 (2023), no. 4, Paper No. 134, 27 pp.
PublicationJournal -
2022
Higher order Brezis-Nirenberg problem on hyperbolic spaces: Existence, nonexistence and symmetry of solutions
Advances in Mathematics 399 (2022), Paper No. 108259, 39 pp.
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2021
Concentration-Compactness Principle for Trudinger–Moser’s Inequalities on Riemannian Manifolds and Heisenberg Groups: A Completely Symmetrization-Free Argument
Advanced Nonlinear Studies 21 (2021), no. 4, 917–937.
PublicationJournal -
2021
The p-ellipticity condition for second order elliptic systems and applications to the Lamé and homogenization problems
Journal of Differential Equations 302 (2021), 367–405.
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2021
Critical and subcritical Trudinger-Moser inequalities on complete noncompact Riemannian manifolds
Advances in Mathematics 389 (2021), Paper No. 107915, 36 pp.
PublicationJournal -
2020
Ground state solutions of polyharmonic equations with potentials of positive low bound
Pacific Journal of Mathematics 305 (2020), no. 1, 353–384.
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2020
Sharp Adams and Hardy-Adams inequalities of any fractional order on hyperbolic spaces of all dimensions
Transactions of the American Mathematical Society 373 (2020), no. 5, 3483–3513.
PublicationJournal -
2018
Sharpened Adams Inequality and Ground State Solutions to the Bi-Laplacian Equation in ℝ⁴
Advanced Nonlinear Studies 18 (2018), no. 3, 429–452.
PublicationJournal -
2018
Fourier analysis and optimal Hardy–Adams inequalities on hyperbolic spaces of any even dimension
Advances in Mathematics 333 (2018), 350–385.
PublicationJournal -
2018
Concentration-compactness principle for Trudinger–Moser inequalities on Heisenberg groups and existence of ground state solutions
Calculus of Variations and Partial Differential Equations 57 (2018), no. 3, Article 84, 26 pp.
Preprints
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2026
A dual variational principle for the Moser-Trudinger inequality: existence, uniqueness and stability of extremals
Preprint, 2026. arXiv:2610.25375.
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2026
Nonconvex Carnot Limit Shapes for Branching Random Walks on the Heisenberg Group
Preprint, 2026. arXiv:2610.23162.
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2026
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2026
Classification of positive entire solutions of the CR Yamabe equation on the Heisenberg group
Preprint, 2026. arXiv:2608.10642.
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2026
Critical Geller Equations on Complex Hyperbolic Space: Sharp Stability, Ground-State Symmetry, and Global Compactness
Preprint, 2026. arXiv:2608.07240.
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2026
Critical GJMS Equations on ℍⁿ × 𝕊ᵐ
Preprint, 2026. arXiv:2607.21451.
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2024
Two-channel global compactness and existence for critical GJMS equations on hyperbolic space
Preprint, 2024, revised 2026. arXiv:2411.14719.
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2021
The Chang-Marshall Trace Inequality for Sobolev functions in domains in higher dimensional space ℝⁿ
Preprint, 2021. arXiv:2108.06792.
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Trudinger-Moser-Adams inequalities for maps between manifolds and applications
Preprint.
Preprint -
—
Hardy-Adams inequalities on product manifolds and applications
Preprint.
Preprint
Teaching experience
University of Science and Technology of China
2022–present Professor- Topics in AnalysisSpring 2026
Spring 2024 - Calculus I exercise course for the China–France Talent Mathematics ClassFall 2025
Spring 2025
Fall 2024
Fall 2022 - Advanced Real AnalysisWinter 2023
- Calculus II exercise course for the China–France Talent Mathematics ClassSpring 2023
Brown University
2019–2022 Tamarkin Assistant Professor- Functions of Several VariablesMATH 1130Fall 2021
- Functions of Several VariablesMATH 1140Fall 2021
- Introductory Calculus IMATH 0090Summer 2021
- Partial Differential EquationsMATH 1120Spring 2021
- Analysis. Functions of One VariableMATH 1010Spring 2021
- Linear AlgebraMATH 0520Spring 2020
- Introductory Calculus IIMATH 0100Spring 2020
Fall 2019
University of Connecticut
2016–2019 Graduate Teaching Assistant- Elementary Differential EquationsMATH 2410Spring 2019
- Calculus for Business and EconomicsMATH 1071QFall 2018
Spring 2018
Spring 2017 - Multivariable CalculusMATH 2110QFall 2017
Fall 2016
Wayne State University
2013–2016 Graduate Teaching Assistant- Elementary FunctionsMAT 1800Winter 2015
Winter 2014 - Algebra with TrigonometryMAT 1050Fall 2014
Spring/Summer 2014
Teaching training. Teaching Mathematics in College, Wayne State University, Fall 2013.
Referee service
Advanced Nonlinear Studies, Annales Polonici Mathematici, Communications on Pure and Applied Analysis, International Mathematics Research Notices, Nonlinear Analysis: Theory, Methods & Applications.
Conference and seminar organization
- Geometric and Functional Inequalities and Applications, online seminar hosted on researchseminars.org. Co-organizer with J. Flynn, N. Lam, and G. Lu.
- Analysis Seminar, Brown University. Co-organizer with J. Pipher and S. Treil.
- AMS Spring Eastern Virtual Sectional Meeting, 20 March 2021. Special Session on Geometric and Functional Inequalities and Nonlinear Partial Differential Equations. Co-organizer with J. Flynn, N. Lam, and G. Lu.
- AMS Fall Central Virtual Sectional Meeting, 12–13 September 2020. Special Session on Geometric Inequalities and Nonlinear Partial Differential Equations. Co-organizer with J. Flynn and G. Lu.
Talks and presentations
- 13 January 2025
Higher order semilinear problems on hyperbolic spaces
3rd International Conference on Geometric and Functional Inequalities and their Applications in PDEs · NJUST
- 30 November 2024
Higher order semilinear problems on hyperbolic spaces
PDE and Geometric Analysis Conference · SWUST
- 19 August 2024
Sobolev and Moser-Trudinger type inequalities on hyperbolic spaces and applications
11th East Asian Conference in Harmonic Analysis and Applications
- 4 November 2023
Hardy-Adams inequalities on product spaces
Fudan–USTC Workshop on Spectrum Geometry
- Spring 2023
Higher order Brezis-Nirenberg problem on hyperbolic spaces
Geometric Analysis Conference · Wuhan University
- 16 January 2023
Symmetry of solutions to higher order and fractional order equations on hyperbolic spaces
1st International Conference on Geometric and Functional Inequalities and their Applications in PDEs · Beijing Institute of Technology
- 2022
Symmetry of solutions to higher order and fractional order equations on hyperbolic spaces
PDE Conference · Anhui University
- 17 August 2022
Symmetry of solutions to higher order semilinear equations with critical growth on hyperbolic spaces
9th East Asian Conference in Harmonic Analysis and Applications
- 20 March 2021
Higher order Brezis-Nirenberg problem on hyperbolic spaces
AMS Spring Eastern Virtual Sectional Meeting
- 12–13 September 2020
Higher order Brezis-Nirenberg problem on hyperbolic spaces
AMS Fall Central Virtual Sectional Meeting
- 13 August 2020
Analysis & PDE Summer Seminar
University of Minnesota, online
- 6–10 January 2020
Higher order Brezis-Nirenberg problem on hyperbolic spaces
Workshop on Harmonic Analysis and Applications · Tsinghua Sanya International Mathematics Forum
- 21 November 2019
Hardy-Sobolev-Maz'ya inequalities and Hardy-Adams inequalities
Analysis Seminar · Worcester Polytechnic Institute
- 13–14 April 2019
Trudinger-Moser inequalities on Riemannian manifolds
AMS Spring Eastern Sectional Meeting · University of Connecticut, Hartford
- 3 April 2019
Analysis Seminar
Brown University
- 29–31 March 2019
Trudinger-Moser inequalities on Riemannian manifolds
Geometric and Harmonic Analysis 2019 · University of Connecticut
- 19–21 October 2018
Trudinger-Moser type inequalities on Riemannian manifolds
Northeastern Analysis Meeting · State University of New York at New Paltz
- 14–15 September 2018
The Chang-Marshall type inequalities for Sobolev functions in any higher dimension
2018 Northeast Analysis Network Conference · University at Albany, SUNY
- 13–15 October 2017
Concentration-compactness Principles on Heisenberg Groups and Riemannian Manifolds
2017 Northeastern Analysis Meeting · University at Albany, SUNY
- 8–13 June 2017
Concentration-compactness Principles on Heisenberg Groups and Riemannian Manifolds
5th Asian Conference of Harmonic Analysis and Application · Hangzhou, China
- 18–19 April 2015
Moser-Trudinger inequality on complete noncompact Riemannian manifold
AMS Spring Western Sectional Meeting · University of Nevada
- 7–8 March 2015
Moser-Trudinger inequality on complete noncompact Riemannian manifold
AMS Spring Eastern Sectional Meeting · Georgetown University
- 28 February–1 March 2015
Best constants for Moser's inequality on noncompact Riemannian manifolds
5th Ohio River Analysis Meeting · University of Cincinnati
Conference and school participation
- 1–21 July 2018
Graduate Summer School, 2018 PCMI Summer Session
Park City, Utah
- 28 April–2 May 2017
Conference on Geometry and Topology in Celebration of the 50th Anniversary of the Journal of Differential Geometry
Harvard University
- 3–4 December 2016
Mini-school on Nonlinear Equations
Harvard University