Uniformly fat sets

Lewis, John L.

doi:10.1090/S0002-9947-1988-0946438-4

Uniformly fat sets
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Trans. Amer. Math. Soc. 308 (1988), 177-196 Request permission

Abstract:

In this paper we study closed sets $E$ which are "locally uniformly fat" with respect to a certain nonlinear Riesz capacity. We show that $E$ is actually "locally uniformly fat" with respect to a weaker Riesz capacity. Two applications of this result are given. The first application is concerned with proving Sobolev-type inequalities in domains whose complements are uniformly fat. The second application is concerned with the Fekete points of $E$.

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