Super log-concavity of the first eigenfunctions for horoconvex domains in hyperbolic space

Wei, Guofang; Xiao, Ling

doi:10.2140/apde.2026.19.1601

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Super log-concavity of the first eigenfunctions for horoconvex domains in hyperbolic space

Guofang Wei and Ling Xiao

Vol. 19 (2026), No. 8, 1601–1612

DOI: 10.2140/apde.2026.19.1601

Abstract

We prove that the first eigenfunction of the Laplacian for a horoconvex domain $Ω \subset ℍ^{n}$ is super log-concave when $diam (Ω)$ is not large. Our result is optimal in the sense that there are counterexamples when $Ω$ is not horoconvex or when $diam (Ω)$ is large.

Keywords

log-concavity, horoconvex domain, eigenfunctions

Mathematical Subject Classification

Primary: 35P15, 58J50

Milestones

Received: 3 January 2025

Revised: 13 August 2025

Accepted: 13 October 2025

Published: 8 October 2026

Authors

Guofang Wei
Department of Mathematics UC Santa Barbara Santa Barbara, CA United States

Ling Xiao
Department of Mathematics University of Connecticut Storrs, CT United States

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Vol. 19, No. 8, 2026