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Super Log-concavity of the First Eigenfunctions for Horo-convex Domains in Hyperbolic Space (2510.13072v1)
Published 15 Oct 2025 in math.AP and math.DG
Abstract: In this paper, we prove that the first eigenfunction of the Laplacian for a horo-convex domain $\Omega\subset\mathbb Hn$ 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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