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

2025/10/15 by Guofang Wei, Ling Xiao, Wei, Guofang +1
Mathematics · #Analytic and geometric function theory #Algebraic and Geometric Analysis #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2510.13072

Abstract

In this paper, we prove that the first eigenfunction of the Laplacian for a horo-convex domain Ω⊂\mathbb Hⁿ is super log-concave when diam(Ω) is not large. Our result is optimal in the sense that there are counterexamples %are constructed for the cases when Ω is not horo-convex or when diam(Ω) is large respectively

Citations

• Spectral Gap Estimates on Conformally Flat Manifolds
• Log-Concavity and Fundamental Gaps on Surfaces of Positive Curvature
• Negative curvature constricts the fundamental gap of convex domains
• The fundamental gap of horoconvex domains in \mathbb Hⁿ
• Sharp Fundamental Gap Estimate on Convex Domains of Sphere

Related

• Log-Concavity of the First Eigenfunction on Horoconvex Domains in the Hyperbolic Plane
• A Priori Log-Concavity Estimates for Dirichlet Eigenfunctions
• Log-Concavity and Fundamental Gaps on Surfaces of Positive Curvature
• Power concavity for elliptic and parabolic boundary value problems on rotationally symmetric domains
• Weinstock inequality in hyperbolic space