Xavier Ramos-Olive -- The Fundamental Gap under integral curvature assumptions

Author information

• Xavier Ramos-Olive
• Worcester Polytechnic Insitute
• Website: https://www.xavieramos.com/

Abstract:

The difference between the first two Dirichlet eigenvalues of the Laplace-Beltrami operator on domains is known by many names: the Fundamental Gap, the Spectral Gap, the Energy Gap, the Mass Gap… Sharp lower bounds for this quantity have been studied extensively for convex domains in Euclidean space and in some manifolds. For non-convex domains, there are non-sharp estimates on manifolds with a pointwise lower bound on the Ricci curvature. We will discuss an extension of these results to domains of manifolds with integral curvature assumptions, which are more stable under perturbations of the metric. This talk is based on joint work with Christian Rose, Lili Wang, and Guofang Wei.

Video Recording:

• [https://fullerton.zoom.us/rec/share/euBdG3iir5eMnhg6Q5tYks2m3TUkyP8gnQUPtEZPK-rMS8wFcGoiiRnXO6o9ez8S.-9E6XU5T4CrRX2-?startTime=1636736444000](https://fullerton.zoom.us/rec/share/euBdG3iir5eMnhg6Q5tYks2m3TUkyP8gnQUPtEZPK-rMS8wFcGoiiRnXO6o9ez8S.-9E6XU5T4CrRX2-?startTime=1636736444000)