%0 Journal Article
%T Isoperimetric inequality for the third eigenvalue of the Laplace-Beltrami operator on $\mathbb S^2$
%A Nikolai Nadirashvili
%A Yannick Sire
%J Mathematics
%D 2015
%I arXiv
%X We prove an Hersch's type isoperimetric inequality for the third positive eigenvalue on $\mathbb S^2$. Our method builds on the theory we developped to construct extremal metrics on Riemannian surfaces in conformal classes for any eigenvalue.
%U http://arxiv.org/abs/1506.07017v3