Publications & Preprints

1. Hamilton-type gradient estimates for Yamabe-type equations on Finsler manifolds. Afrika Matematika. 36, 134 (2025),  with S. Huang, X. Liu, B. Shen.  https://doi.org/10.1007/s13370-025-01355-0

2. Li-Yau estimates for a nonlinear parabolic equation on Finsler metric measure spaces. Manuscripta Mathematica. 176, 22 (2025),  with B. Shen.  https://doi.org/10.1007/s00229-025-01615-0

3. Nonlinear eigenvalue problems for a class of quasilinear operator on complete Riemannian manifolds, with B. Shen, arXiv:2502.05426

4. Feasibility of Nash--Moser iteration for Cheng--Yau-type gradient estimates of nonlinear equations on complete Riemannian manifolds, with B. Shen, arXiv:2405.10344

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Lecture notes

• PDEs. These notes are from reading seminar of Evans' PDE in 2022-2023. It contains Chapter 5 - 7, Sobolev Space and "Big Three" (elliptic, parabolic and hyperbolic equation.), and part of Chapter 8 for nonlinear case. In addition, some answers for  the problems in Chapter 6 and 7.

• A small talk on De Rham Cohomology and Euler Characteristic.

• Riemannian Geometry, based on the textbook by do Carmo and notes on Differential Manifold when I was studying Lectures on Differential Geometry by Chern. 

• Geometric Analysis, the lecture notes in Spring 2023, based on the classic textbook by Peter Li. The video recordings of the lecture can be seen on Bilibili (in Chinese).

• Convergence of manifolds, from the lectures by Brian Allen in VIASM-ICTP summer school in 2023, introduces different types of convergence such as Gromov-Hausdorff convergence, flat convergence, and Sormani-Wenger intrinsic flat (SWIF) convergence .

• Here  is some of answers  (in Chinese)  for Differential Geometry of Curves and Surfaces, do Carmo. I typed these notes when I was a TA in Spring 2022.

• Stokes' Theorem on Manifolds (in Chinese). I gave a short lecture on this topic in Spring 2022, covering elemental tensor calculation and smooth manifold. 

Last Updated: Aug 2025