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Spring 2009 Duality, uniformity, and linear local connectivity
Shanshuang Yang
Illinois J. Math. 53(1): 339-347 (Spring 2009). DOI: 10.1215/ijm/1264170854

Abstract

Using Väisälä’s metric duality on joinability of sets, we show, among other things, that in $\mathbb{R}^3$ if the complementary domains of a surface are LLC, they are also uniform. As an application, we show that an Ahlfors regular topological sphere that admits a quasiconformal reflection is quasisymmetrically equivalent to the standard sphere.

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Shanshuang Yang. "Duality, uniformity, and linear local connectivity." Illinois J. Math. 53 (1) 339 - 347, Spring 2009. https://doi.org/10.1215/ijm/1264170854

Information

Published: Spring 2009
First available in Project Euclid: 22 January 2010

zbMATH: 1192.30006
MathSciNet: MR2584950
Digital Object Identifier: 10.1215/ijm/1264170854

Subjects:
Primary: 30C65 , 55M05

Rights: Copyright © 2009 University of Illinois at Urbana-Champaign

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Vol.53 • No. 1 • Spring 2009
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