Vanishing of the fundamental gap for (horo)convex domains in hyperbolic space

Friday, February 26, 2021 - 12:00pm to 1:00pm

Speaker

Xuan Hien Nguyen
Associate Professor
Iowa State University

Abstract

For the Laplace operator with Dirichlet boundary conditions on convex domains in $H^n, n ≥ 2$, we prove that the product of the fundamental gap with the square of the diameter can be arbitrarily small for domains of any diameter. This property distinguishes hyperbolic spaces from Euclidean and spherical ones, where the quantity is bounded below by $3 \pi^2$. We finish by talking about horoconvex domains. 

Description

Contact Julien Paupert for the Zoom link.

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