Journal of Differential Geometry

Maximizing Steklov eigenvalues on surfaces

Romain Petrides

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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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J. Differential Geom., Volume 113, Number 1 (2019), 95-188.

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

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Petrides, Romain. Maximizing Steklov eigenvalues on surfaces. J. Differential Geom. 113 (2019), no. 1, 95--188. doi:10.4310/jdg/1567216955.

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