Isoperimetric inequality for the third eigenvalue of the Laplace-Beltrami operator on $\mathbb S^2$
Differential Geometry
2016-08-22 v5
Abstract
We prove an Hersch's type isoperimetric inequality for the third positive eigenvalue on . Our method builds on the theory we developped to construct extremal metrics on Riemannian surfaces in conformal classes for any eigenvalue.
Keywords
Cite
@article{arxiv.1506.07017,
title = {Isoperimetric inequality for the third eigenvalue of the Laplace-Beltrami operator on $\mathbb S^2$},
author = {Nikolai Nadirashvili and Yannick Sire},
journal= {arXiv preprint arXiv:1506.07017},
year = {2016}
}
Comments
in v2, we simplified the proof of Theorem 3.1