Affiliation:
1. Department of Mathematical Sciences , University of Cincinnati , Cincinnati , U.S.A.
Abstract
Abstract
The sphericalization procedure converts a Euclidean space into a compact sphere. In this note we propose a variant of this procedure for locally compact, rectifiably path-connected, non-complete, unbounded metric spaces by using conformal deformations that depend only on the distance to the boundary of the metric space. This deformation is locally bi-Lipschitz to the original domain near its boundary, but transforms the space into a bounded domain. We will show that if the original metric space is a uniform domain with respect to its completion, then the transformed space is also a uniform domain.
Subject
Applied Mathematics,Geometry and Topology,Analysis
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