PreprintCC BY 4.0arXiv
Power convexity of the torsion function on horo-convex domains in hyperbolic space
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 −√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.
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BibTeX
@misc{zhang2026power,
title = {{Power convexity of the torsion function on horo-convex domains in hyperbolic space}},
author = {Wei Zhang and Qi Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02516},
eprint = {2609.02516},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02516},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Power convexity of the torsion function on horo-convex domains in hyperbolic space
AU - Wei Zhang
AU - Qi Zhou
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02516
UR - https://arxiv.org/abs/2609.02516
AB - 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 −√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.
ER -