On the fundamental gap and convex sets in hyperbolic space

Abstract: The lower bound on the fundamental gap of the Laplacian on convex domains in R^n, with Dirichlet boundary conditions, has a long history and has been finally settled a few years ago with parabolic methods by Andrews and Clutterbuck. More recently, the same lower bound, which depends on the diameter of the domain, has been proved for convex sets on the standard sphere in several stages with several groups of authors, 2016-2018. Over the past year, together with collaborators, we have found that the gap on the hyperbolic space behaves strikingly different and we aim to explain it, particularly for this audience, as a difference in the nature of convex sets in H^n versus R^n or S^n.

analysis of PDEsmetric geometry

Audience: researchers in the topic

Online asymptotic geometric analysis seminar

Series comments: The link: technion.zoom.us/j/99202255210

If you are interested in giving a talk, please let one of the organizers know. Also, please suggest speakers which you would like to hear talk. Most talks are 50 minutes, but some 20-minute talks will be paired up as well. The talks will be video recorded conditioned upon the speakers' agreement.