Welcome to my homepage! I received my PhD from Nanjing University in June 2024. From September 2024 to August 2026, I was a Postdoctoral Fellow at CUHK. Since September 2026, I have been a Research Assistant Professor at PolyU.

Email

  • mingxiang.li@polyu.edu.hk

Employment

  • The Hong Kong Polytechnic University, Sep.2 2026-Current, Research Assistant Professor
  • The Chinese University of Hong Kong, Sep.2 2024 -Sep. 1 2026, PostDoc Fellow

Education

  • Nanjing University, Sep 2019 - Jun 2024, Ph.D.
  • University Paul Sabatier, Oct 2022 - Aug 2023, Visiting PhD student
  • Nanjing University, Sep 2015 - Jun 2019, Bachelor

Preprints

  1. (With Quoc Anh Ngo, Xingwang Xu) Remarks on prescribed scalar curvature functions, arxiv:2610.19667
  2. (With Guosheng Jiang, Zhehui Wang ) A Cheng-Yau type estimate for positive biharmonic functions, arxiv: 2609.05965
  3. (With Liuwei Gong, Juncheng Wei) A counterexample to a strong maximum principle for the sixth-order GJMS operator, arxiv: 2608.24148
  4. (With Xumin Jiang, Zhehui Wang ) On the proof of Bray’s conjecture, arxiv:2608.20215
  5. On the positivity of Yamabe invariant and Paneitz operator, arxiv:2608.09279
  6. (With Xumin Jiang, Zhehui Wang ) Bonnet-Myers type theorems for $Q$-curvature on four-manifolds, arxiv:2607.25343
  7. (With Xingwang Xu) A sharp isoperimetric inequality and the top order $Q$-curvature, arxiv:2607.06951
  8. (With Kui Li, Juncheng Wei) On a new region for the Lane-Emden conjecture in higher dimensions, arxiv:2510.06613 (Submitted to a Chinese-language journal. The complete proof has recently been claimed by OpenAI link )
  9. (With Juncheng Wei, Xingwang Xu) On geometry of $Q_{2k}^{g}$-curvature, arxiv:2506.20165
  10. (With Biao Ma) Existence of complete conformal metrics on $\mathbb{R}^n$ with prescribed Q-curvature, arxiv:2503.23689
  11. The total Q-curvature, volume entropy and polynomial growth polyharmonic functions (II), arxiv:2408.03640
  12. Conformal metrics with finite total Q-curvature revisited, arxiv: 2405.09872

Publications

  1. (With Pak-Yeung Chan, Man-Chun Lee) Volume growth and integral curvature bound for non-negatively curved three-manifolds, College Mathematics 1, no. 1 (2026): 64-88. (special volume in memory of L.-F. Tam) pdf arxiv:2609.24096
  2. (With Juncheng Wei) Higher order Bol’s equality and its applications, arxiv:2308.11388, to appear in Acta Math. Sin. (Engl. Ser.)
  3. Obstructions to prescribed Q-curvature of complete conformal metrics on $\mathbb{R}^n$, Rev. Mat. Iberoam. 42 (2026), no. 1, pp. 75–94. pdf arXiv:2401.03457
  4. (With Xingwang Xu) On positivity of the $Q$-curvatures of conformal metrics, J. Funct. Anal. 289 (2025), no. 8, Paper No. 111011, 23 pp. pdf arXiv:2402.16277
  5. Asymptotic behavior of conformal metrics with null Q-curvature, J. Geom. Anal. 35 (2025), no. 5, Paper No. 145. pdf arXiv:2308.12656
  6. (With Juncheng Wei) A remark on the Case-Gursky-Vetois identity and its applications, Proc. Amer. Math. Soc. 153 (2025), no. 08, 3417–3430. pdf arXiv:2410.09393
  7. (With Yuxin Ge, Zhao Lian) A new invariant on 3-dimensional manifolds and applications, Commun. Contemp. Math. 27 (2025), no. 5, 2450036. pdf
  8. The total Q-curvature, volume entropy and polynomial growth polyharmonic functions, Advance in Mathematics 450 (2024), Paper No. 109768. pdf arXiv:2306.15623
  9. A Liouville-type theorem in conformally invariant equations, Math. Ann. 389 (2024), no. 3, 2499–2517. pdf arXiv:2306.15754
  10. (With Xingwang Xu) Asymptotic behavior of conformal metrics on torus, Discrete Contin. Dyn. Syst. 44 (2024), no. 5, 1376–1394. pdf
  11. A note on prescribed Q-curvature, Pacific J. Math. 319 (2022), no. 1, 181–188. pdf
  12. (With Xingwang Xu) A flow approach to mean field equation, Calc. Var. Partial Differential Equations 61 (2022). pdf
  13. (With Xuezhang Chen, Zirui Li, Xingwang Xu) On Gaussian curvature flow, J. Differential Equations 294 (2021). pdf

Survey

  1. Mingxiang Li, Xingwang Xu, Starting with the triangle（从三角形说起）, 2022. 数学所讲座.2018[M]. 北京：科学出版社，link.