The fundamental gap of horoconvex domains in \mathbb Hⁿ

2021/01/25 by Xuan Hien Nguyen, Nguyen, Xuan Hien, Alina Stancu +3 · 2 citations
Mathematics · #35P15 #53C35 #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2101.10176

openalex publication_date 2021/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that, for horoconvex domains in the hyperbolic space, the product of their fundamental gap with the square of their diameter has no positive lower bound. The result follows from the study of the fundamental gap of geodesic balls as the radius goes to infinity. In the process, we improve the lower bound for the first eigenvalue of balls in hyperbolic space.

Citations

• Power concavity for elliptic and parabolic boundary value problems on rotationally symmetric domains

Cited by

• Super Log-concavity of the First Eigenfunctions for Horo-convex Domains in Hyperbolic Space
• On the PPW Conjecture For Hopf-symmetric Sets In Non-compact Rank One Symmetric Space

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