Porous sets and quasisymmetric maps

Väisälä, Jussi

doi:10.1090/S0002-9947-1987-0869219-8

Porous sets and quasisymmetric maps
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Trans. Amer. Math. Soc. 299 (1987), 525-533 Request permission

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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