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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Porous sets and quasisymmetric maps


Author: Jussi Väisälä
Journal: Trans. Amer. Math. Soc. 299 (1987), 525-533
MSC: Primary 30C60
MathSciNet review: 869219
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Abstract: A set $ A$ in $ {R^n}$ is called porous if there is $ \alpha > 0$ such that every ball $ \overline B (x,r)$ contains a point whose distance from $ A$ is at least $ \alpha r$. We show that porosity is preserved by quasisymmetric maps, in particular, by bilipschitz maps. Local versions are also given.


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DOI: https://doi.org/10.1090/S0002-9947-1987-0869219-8
Keywords: Porous, quasisymmetric, bilipschitz
Article copyright: © Copyright 1987 American Mathematical Society