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

Quantitative estimates for the relative isoperimetric problem and its gradient flow outside convex bodies in the plane, with Elena Mäder-Baumdicker, Robin Neumayer, and Melanie Rupflin, Preprint.  (ArXiv link)

Quantitative rigidity using Colding's monotonicity formulas for Ricci curvature, with Christine Breiner, Preprint. (ArXiv link)

Monotonicity formulas and Hessian of the Green function, Preprint. (ArXiv link)

A Matrix Li-Yau-Hamilton estimate for the Green function on Kähler manifolds, International Mathematics Research Notices, Volume 2024 (2024), Issue 10, 8230--3239. (ArXiv link) (journal link)

Canonical Identification at Infinity for Ricci-flat Manifolds, Journal of Geometric Analysis, Volume 32 (2022), 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)