Research Interests

My primary research interest is in geometric analysis, which is a field that combines ideas and techniques from various fields including differential and algebraic geometry, partial differential equations, functional analysis, and mathematical physics. Currently I am interested in geometric flows, especially the mean curvature flow, and the convergence of manifolds with curvature bounds to possibly singular spaces, especially Ricci limit spaces, and Kähler geometry.

Publications & Preprints

A Matrix Li-Yau-Hamilton estimate for the Green function on Kähler manifolds, to appear in IMRN. (ArXiv link) 

Canonical Identification at Infinity for Ricci-flat Manifolds, Journal of Geometric Analysis, -published online in Volume 32 (2021), article 8. (ArXiv link)(journal link)

A Compactness Theorem for Rotationally Symmetric Riemannian Manifolds with Positive Scalar Curvature, with Wenchuan Tian and Changliang Wang, Pure and Applied Mathematics Quarterly, Volume 14 (2019), Number 3--4, 529--561. (ArXiv link)(journal link)

Matrix Inequality for the Laplace Equation, International Mathematics Research Notices, Volume 2019 (2019), Issue 11, 3485--3497. (ArXiv link)(journal link)