11 citations · 23 across the 16 of their papers we have counts for
4 papers · 1 filter
Negative curvature constricts the fundamental gap of convex domains
Gabriel Khan, Xuan Hien Nguyen
We consider the Laplace-Beltrami operator with Dirichlet boundary conditions on convex domains in a Riemannian manifold , and prove that the product of the fundamental gap…
Log-Concavity and Fundamental Gaps on Surfaces of Positive Curvature
Gabriel Khan, Xuan Hien Nguyen, Malik Tuerkoen +1
We study the log-concavity of the first Dirichlet eigenfunction of the Laplacian for convex domains. For positively curved surfaces satisfying a condition involving the curvature a…
When Optimal Transport Meets Information Geometry
Gabriel Khan, Jun Zhang
Information geometry and optimal transport are two distinct geometric frameworks for modeling families of probability measures. During the recent years, there has been a surge of r…
An Illustrated Introduction to the Ricci Flow
Gabriel Khan
The Ricci flow is one of the most important topics in differential geometry, and a central focus of modern geometric analysis. In this paper, we give an illustrated introduction to…