The Weinstock inequality for convex domains in hyperbolic space

Jin Sun; Lili Wang; Tao Wang

The Weinstock inequality for convex domains in hyperbolic space

Spectral Theory 2026-08-11 v1 Differential Geometry

Authors: Jin Sun , Lili Wang , Tao Wang

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 $n\geq 3$ .

Keywords

Weinstock inequality Steklov eigenvalue convex domains hyperbolic space one-crossing property

Cite

@article{arxiv.2608.10771,
  title  = {The Weinstock inequality for convex domains in hyperbolic space},
  author = {Jin Sun and Lili Wang and Tao Wang},
  journal= {arXiv preprint arXiv:2608.10771},
  year   = {2026}
}