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September 2019 Maximizing Steklov eigenvalues on surfaces
Romain Petrides
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J. Differential Geom. 113(1): 95-188 (September 2019). DOI: 10.4310/jdg/1567216955

Abstract

We study the Steklov eigenvalue functionals $\sigma_k (\Sigma, g) L_g (\partial \Sigma)$ on smooth surfaces with non-empty boundary. We prove that, under some natural gap assumptions, these functionals do admit maximal metrics which come with an associated minimal surface with free boundary from $\Sigma$ into some Euclidean ball, generalizing previous results by Fraser and Schoen in [“Sharp eigenvalue bounds and minimal surfaces in the ball,” Invent. Math., 203(3):823–890, 2016].

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Romain Petrides. "Maximizing Steklov eigenvalues on surfaces." J. Differential Geom. 113 (1) 95 - 188, September 2019. https://doi.org/10.4310/jdg/1567216955

Information

Received: 20 February 2016; Published: September 2019
First available in Project Euclid: 31 August 2019

zbMATH: 07104704
MathSciNet: MR3998908
Digital Object Identifier: 10.4310/jdg/1567216955

Rights: Copyright © 2019 Lehigh University

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Vol.113 • No. 1 • September 2019
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