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arXiv · 2409.02766

Weinstock inequality in hyperbolic space

Pingxin Gu·Haizhong Li·Yao Wan
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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 $\mathbb{H}^n$ for $n \geq 4$. In particular, when the domain is convex, our result gives an affirmative answer to Open Question 4.27 in [7] for the hyperbolic space $\mathbb{H}^n$ when $n \geq 4$.

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Pingxin Gu, Haizhong Li, Yao Wan. 2024-09-04. Weinstock inequality in hyperbolic space. https://arxiv.org/abs/2409.02766

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