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arXiv · 2608.11849

Weinstock inequality in hyperbolic space II

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 $n\geq 3$. We note that when $n\geq 4$, the result was obtained in our previous paper [23]. In particular, when the domain is convex, our result gives an affirmative answer to Open Question 4.27 in [13] for the hyperbolic case.

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Pingxin Gu, Haizhong Li, Yao Wan. 2026-08-12. Weinstock inequality in hyperbolic space II. https://arxiv.org/abs/2608.11849

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