Work

Power convexity of the torsion function on horo-convex domains in hyperbolic space

Year: 2026

Type: preprint

Abstract: In this paper, we study the torsion problem on bounded, smooth, strictly horo-convex domains in hyperbolic space. We prove that if the diameter of the domain is sufficiently small, then $-\sqrt{u}$ is strictly convex, where $u$ denotes the torsion function. The main ingredients of our proof are the constant rank theorem, a boundary convexity estimate, and a deformation argument for the domain. We also show that the exponent $1/2$ is optimal, even among strictly horo-convex domains of arbitrarily small diameter.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.02516

Authors: Zhang, Wei, Zhou, Qi

Institution: Lanzhou University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7207801628

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