The Weinstock inequality for convex domains in hyperbolic space

Jin Sun; Lili Wang; Tao Wang

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arXiv · 2608.10771

The Weinstock inequality for convex domains in hyperbolic space

Jin Sun·Lili Wang·Tao Wang

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Abstract

We prove the Weinstock inequality for the first Steklov eigenvalue of convex domains in hyperbolic space $\mathbb{H}^{n}$, resolving Open Question 4.27 of Colbois-Girouard-Gordon-Sher(2024) for the remaining case $n=3$. Our argument replaces the global monotonicity required in earlier work Gu-Li-Wan(2025) with a one-crossing property, which is established via an explicit slope comparison. The proof works uniformly for all $n\geq 3$.

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BibTeX RIS

Jin Sun, Lili Wang, Tao Wang. 2026-08-11. The Weinstock inequality for convex domains in hyperbolic space. https://arxiv.org/abs/2608.10771

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