On the isoperimetric inequality for the first positive Neumann eigenvalue on the sphere

Abstract

We prove that geodesic disks are the unique maximizers of the first positive Neumann eigenvalue among all simply connected domains in ${\mathbb{S}}^2$ with prescribed area. We then show that geodesic disks are no longer maximisers for the class of spherical annuli.

arXiv commentThe paper is an improvement of the previous version