Associate Professor
(205) 934-2154
University Hall 4006
Research and Teaching Interests: Geometric analysis, Differential geometry, Partial differential equations
Office Hours: By appointment and through email
Education:
- Ph.D., University of Oklahoma, Mathematics
I was born in China and got my B.A. from Wuhan University, Hubei Province, China. I got my Ph.D. in Mathematics from University of Oklahoma. I always found the idea of using Partial Differential Equations to solve problems from Differential Geometry fascinating.
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Select Publications
- A volume preserving flow and the isoperimetric problem in warped product spaces, (with Pengfei Guan, Mu-Tao Wang), to appear in Transactions of the American Mathematical Society.
- An integral formula and its applications on sub-static manifolds, (with Chao Xia). To appear in Journal of Differential Geometry.
- A fully-nonlinear flow and quermassintegral inequalities, (with Pengfei Guan). SCIENTIA SINICA Mathematica, Vol. 48, Iss. 1, 2018.
- An integral formula for affine connections, (with Chao Xia). Journal of Geometric Analysis, Volume 27, Issue 3, pp 2539–2556, 2017.
- A new mean curvature type of flow in space forms, (with Pengfei Guan), International Mathematics Research Notices, 2015, no. 13, 4716-4740.
- Hypersurfaces of Prescribed Curvature Measure (with Pengfei Guan and Yanyan Li), Duke Mathematical Journal, Volume 161, Number 10, 2012.
- A geometrical characterization of sharp Hardy inequalities (with Roger Lewis and Yanyan Li), Journal of Functional Analysis, Volume 262, Issue 7, 1 April 2012.
- Differential Harnack inequalities on Riemannian manifolds I : linear heat equation (with Xiangjin Xu), Advances in Mathematics, Volume 226, Issue 5, 2011.
- The quermassintegral inequalities for starshaped domains (with Pengfei Guan), Advances in Mathematics 221 (2009), 1725-1732
- Eigenvalues and energy functionals with monotonicity formulae under Ricci flow, Mathematische Annalen, 338 (2007), 927-946.
- Sharp local embedding inequalities (with Meijun Zhu), Comm. Pure Appl. Math. 59 (2006), no. 1, 122--144.