Weinstock inequality in hyperbolic space

2024/09/04 by Pingxin Gu, Haizhong Li, Gu, Pingxin +3 · 1 citation
Mathematics · #Mathematics and Applications #Functional Equations Stability Results #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2409.02766

Abstract

In this paper, we establish the Weinstock inequality for the first non-zero Steklov eigenvalue on star-shaped mean convex domains in hyperbolic space ℍⁿ for n ≥ 4. In particular, when the domain is convex, our result gives an affirmative answer to Open Question 4.27 in [7] for the hyperbolic space ℍⁿ when n ≥ 4.

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• Payne-Philippin's overdetermined problems on compact surfaces

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