Abstract
We prove Hersch’s type isoperimetric inequality for the third positive eigenvalue on $\mathbb{S}^2$. Our method builds on the theory we developed to construct extremal metrics on Riemannian surfaces in conformal classes for any eigenvalue.
Citation
Nikolai Nadirashvili. Yannick Sire. "Isoperimetric inequality for the third eigenvalue of the Laplace–Beltrami operator on $\mathbb{S}^2$." J. Differential Geom. 107 (3) 561 - 571, November 2017. https://doi.org/10.4310/jdg/1508551225
Information
