3 papers
math.AP2025
A Priori Log-Concavity Estimates for Dirichlet Eigenfunctions
Gabriel Khan, Soumyajit Saha, Malik Tuerkoen
In this paper, we establish a priori log-concavity estimates for the first Dirichlet eigenfunction of convex domains of a Riemannian manifold. Specifically, we focus on cases where…
math.DG2024
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…
math.DG2024
Spectral Gap Estimates on Conformally Flat Manifolds
Gabriel Khan, Malik Tuerkoen
The fundamental gap is the difference between the first two Dirichlet eigenvalues of a Schrödinger operator (and the Laplacian, in particular). For horoconvex domains in hyperboli…