Characterizations for the existence of traces of first-order Sobolev spaces on hyperbolic fillings

2022/03/27 by Huang, Manzi, Xu, Zhihao · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2203.14231

Abstract

In this paper, we study the existence of traces for Sobolev spaces on the hyperbolic filling X of a compact metric space Z equipped with a doubling measure. Given a suitable metric on X, we can regard Z as the boundary of X. After equipping X with a weighted measure μ via the measure on Z and the Euclidean arc length, we give characterizations for the existence of traces for first-order Sobolev spaces.

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• Quantitative correspondence between quasi-symmetric mappings on complete metric spaces and rough quasi-isometric mappings on their hyperbolic fillings

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