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<p>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 with a flat Euclidean boundary when the scalar curvature of the compactified metric has a designated sign.</p>

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Liouville-type theorems on the hyperbolic space

  • 期刊论文

  • 发表日期：

    2025年8月20日

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  • Sanghoon Lee

摘要

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 with a flat Euclidean boundary when the scalar curvature of the compactified metric has a designated sign.