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arXiv · 2510.13072

Super Log-concavity of the First Eigenfunctions for Horo-convex Domains in Hyperbolic Space

Guofang Wei·Ling Xiao
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Abstract

In this paper, we prove that the first eigenfunction of the Laplacian for a horo-convex domain $\Omega\subset\mathbb H^n$ is super log-concave when $\text{diam}(\Omega)$ is not large. Our result is optimal in the sense that there are counterexamples %are constructed for the cases when $\Omega$ is not horo-convex or when $\text{diam}(\Omega)$ is large respectively

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Guofang Wei, Ling Xiao. 2025-10-15. Super Log-concavity of the First Eigenfunctions for Horo-convex Domains in Hyperbolic Space. https://arxiv.org/abs/2510.13072

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