Isoperimetric inequality for the third eigenvalue of the Laplace-Beltrami operator on $\mathbb S^2$

Nikolai Nadirashvili; Yannick Sire

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arXiv · 1506.07017

Isoperimetric inequality for the third eigenvalue of the Laplace-Beltrami operator on $\mathbb S^2$

Nikolai Nadirashvili·Yannick Sire

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Abstract

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.

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BibTeX RIS

Nikolai Nadirashvili, Yannick Sire. 2016-08-19. Isoperimetric inequality for the third eigenvalue of the Laplace-Beltrami operator on $\mathbb S^2$. https://arxiv.org/abs/1506.07017

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