Sharp functional inequalities
Sobolev, Hardy–Sobolev–Maz’ya, Trudinger–Moser, and Adams inequalities on Riemannian and sub-Riemannian manifolds.
Professor of Mathematics
Jungang Li
School of Mathematical Sciences
University of Science and Technology of China
My research lies in nonlinear analysis and geometric partial differential equations, with a focus on sharp functional inequalities.
jungangli@ustc.edu.cn
Nonlinear analysisGeometric PDEsFunctional inequalities
Hefei, China
Research interests
Analysis on geometric spaces
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.
Research papers
Publications & preprints
24 works 14 publications and 10 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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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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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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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
The Chang-Marshall Trace Inequality for Sobolev functions in domains in higher dimensional space ℝⁿ
Preprint, 2021. arXiv:2108.06792.
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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.
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Trudinger-Moser-Adams inequalities for maps between manifolds and applications
Preprint.
Preprint -
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Hardy-Adams inequalities on product manifolds and applications
Preprint.
Preprint
No papers match this search.
In the classroom
Teaching
Courses in analysis, differential equations, linear algebra, and calculus, at USTC and previously at Brown, Connecticut, and Wayne State.
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
Earlier teaching at Brown, Connecticut & Wayne State
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
Academic background
About me
I am a professor in the School of Mathematical Sciences at USTC, where I have worked since 2022.
I received my Ph.D. from the University of Connecticut in 2019, advised by Professor Guozhen Lu. I then joined Brown University as a Tamarkin Assistant Professor, working with Professor Jill Pipher. My undergraduate studies were at Zhejiang University, advised by Professor Weimin Sheng.
Beyond mathematics, I enjoy basketball and philosophy, and I am interested in the connections between artificial intelligence and mathematics.
2022–present
Professor
University of Science and Technology of China
2019–2022
Tamarkin Assistant Professor
Brown University · Mentor Professor Jill Pipher
2016–2019
Ph.D. in Mathematics
University of Connecticut · Advisor Professor Guozhen Lu
2009–2013
B.S. in Applied Mathematics
Zhejiang University · Advisor Professor Weimin Sheng
Conferences & seminars
Selected talks
- 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
School of Mathematical Sciences, Room 418
University of Science and Technology of China
Hefei, Anhui, China