Research Interests

Conformal geometry Quantitative stability Mean curvature Bubble towers Yamabe problem T-curvature Ancient solutions Sobolev inequalities Scalar curvature Harmonic maps Q-curvature Blow-up analysis Unit ball Nondegeneracy Curvature flows Paneitz operator Nodal solutions Manifolds with boundary Energy-critical heat equation Conformal metrics Extremal metrics Brezis-Nirenberg problem Yamabe flow Classification theorems Elliptic PDE Sobolev trace inequalities Half-harmonic maps Hardy-Sobolev inequality Sharp constants Fractional equations Degenerate operators Higher-order equations

Preprints

  1. Liming Sun, Heming Wang, Shihong Zhang, Conformal Metrics on the Unit Ball with Constant \(Q\)-Curvature, Constant \(T\)-Curvature, and Minimal Boundary, arXiv:2608.23106.

  2. Pak Tung Ho, Cheikh Birahim Ndiaye, Liming Sun, Heming Wang, Prescribed \(T\)-Curvature Flow on the Four-Dimensional Unit Ball, arXiv:2601.22934.

  3. Liming Sun, Jun-cheng Wei, Wen Yang, On Brezis’ First Open Problem: A Complete Solution, arXiv:2503.06904.

Published

  1. Yuanli Li, Liming Sun, Planar doubling nodal solutions to the Yamabe equation with maximal rank, Journal of Differential Equations 483, 114751 (2026).

  2. Tongtong Li, Liming Sun, Shumao Wang, A slow blow-up solution for the four dimensional energy critical semilinear heat equation, Calculus of Variations and Partial Differential Equations 65(5), 142 (2026).

  3. Liming Sun, Jun-cheng Wei, Wen Yang, On the 3-D Brezis–Nirenberg problem with small parameter, Communications in Contemporary Mathematics 28(5), 1–34 (2026).

  4. Kyeongsu Choi, Liming Sun, Classification of ancient flows by sub-affine-critical powers of curvature in \(\mathbb{R}^2\), Journal of Functional Analysis 288(9), 110865 (2025).

  5. Bin Deng, Liming Sun, Jun-cheng Wei, Sharp quantitative estimates of Struwe’s decomposition, Duke Mathematical Journal 174(1), 159–228 (2025).

  6. Liming Sun, Lei Wang, Attainability of the best constant of Hardy–Sobolev inequality with full boundary singularities, Journal of the London Mathematical Society 111(2), 1–42 (2025).

  7. Cheikh Birahim Ndiaye, Liming Sun, Explicit forms for extremals of sharp Sobolev trace inequalities on the unit balls, Calculus of Variations and Partial Differential Equations 63(7), 181 (2024).

  8. Bin Deng, Liming Sun, Jun-cheng Wei, Quantitative stability of harmonic maps from \(\mathbb{R}^2\) to \(\mathbb{S}^2\) with a higher degree, Calculus of Variations and Partial Differential Equations 63(4), 101 (2024).

  9. Bin Deng, Liming Sun, Jun-cheng Wei, Non-degeneracy and quantitative stability of half-harmonic maps from ℝ to 𝕊, Advances in Mathematics 420, 108979 (2023).

  10. Jingbo Dou, Liming Sun, Lei Wang, Meijun Zhu, Divergent operator with degeneracy and related sharp inequalities, Journal of Functional Analysis 282(2), 109294 (2022).

  11. Liming Sun, Jun-cheng Wei, Qidi Zhang, Bubble towers in the ancient solution of energy-critical heat equation, Calculus of Variations and Partial Differential Equations 61(6), 1–47 (2022).

  12. Kyeongsu Choi, Liming Sun, Ancient finite entropy flows by powers of curvature in \(\mathbb{R}^2\), Nonlinear Analysis, Theory, Methods and Applications 216, 1–19 (2022).

  13. Cheikh Birahim Ndiaye, Yannick Sire, Liming Sun, Uniformization theorems: Between Yamabe and Paneitz, Pacific Journal of Mathematics 314(1), 115–159 (2021).

  14. Joel Spruck, Liming Sun, Convexity of 2-convex translating solitons to the mean curvature flow in \(\mathbb{R}^{n+1}\), Journal of Geometric Analysis 31(4), 4074–4091 (2021).

  15. Sergio Almaraz, Liming Sun, Convergence of the Yamabe flow on manifolds with minimal boundary, Annali della Scuola Normale Superiore di Pisa, 1197–1272 (2020).

  16. Hardy Chan, Yannick Sire, Liming Sun, Convergence of the fractional Yamabe flow for a class of initial data, Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, 1703–1740 (2020).

  17. Xuezhang Chen, Yuping Ruan, Liming Sun, The Han-Li conjecture in constant scalar curvature and constant boundary mean curvature problem on compact manifolds, Advances in Mathematics 358, 106854 (2019).

  18. Xuezhang Chen, Liming Sun, Existence of conformal metrics with constant scalar curvature and constant boundary mean curvature on compact manifolds, Communications in Contemporary Mathematics 21(3), 1850021 (2019).

  19. Xuezhang Chen, Pak Tung Ho, Liming Sun, Prescribed scalar curvature plus mean curvature flows in compact manifolds with boundary of negative conformal invariant, Annals of Global Analysis and Geometry 53(1), 121–150 (2018).

  20. Liming Sun, Jingang Xiong, Classification theorems for solutions of higher order boundary conformally invariant problems, I, Journal of Functional Analysis 271(12), 3727–3764 (2016).