Journal of Differential Geometry

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

Nikolai Nadirashvili and Yannick Sire

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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.

Article information

Source
J. Differential Geom., Volume 107, Number 3 (2017), 561-571.

Dates
Received: 19 June 2015
First available in Project Euclid: 21 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1508551225

Digital Object Identifier
doi:10.4310/jdg/1508551225

Mathematical Reviews number (MathSciNet)
MR3715349

Zentralblatt MATH identifier
1385.53027

Citation

Nadirashvili, Nikolai; Sire, Yannick. Isoperimetric inequality for the third eigenvalue of the Laplace–Beltrami operator on $\mathbb{S}^2$. J. Differential Geom. 107 (2017), no. 3, 561--571. doi:10.4310/jdg/1508551225. https://projecteuclid.org/euclid.jdg/1508551225


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Lehigh University

International Press

Journal of Differential Geometry

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