Liouville-Type Theorems on the Hyperbolic Space
Differential Geometry
2024-01-15 v1 Analysis of PDEs
Abstract
In this paper, we establish Liouville-type theorems for a one-parameter family of elliptic PDEs on the standard upper half-plane model of the hyperbolic space, under specific geometric assumptions. Our results indicate that the Euclidean half-plane is the only compactification of the hyperbolic space when the scalar curvature of the compactified metric has a designated sign.
Keywords
Cite
@article{arxiv.2401.06623,
title = {Liouville-Type Theorems on the Hyperbolic Space},
author = {Sanghoon Lee},
journal= {arXiv preprint arXiv:2401.06623},
year = {2024}
}
Comments
21 pages, all comments welcome!