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- W3214377029 abstract "In this paper we construct a large family of examples of subsets of Euclidean space that support a 1-Poincar'e inequality yet have empty interior. These examples are formed from an iterative process that involves removing well-behaved domains, or more precisely, domains whose complements are uniform in the sense of Martio and Sarvas. While existing arguments rely on explicit constructions of Semmes families of curves, we include a new way of obtaining Poincar'e inequalities through the use of relative isoperimetric inequalities, after Korte and Lahti. To do so, we further introduce the notion of of isoperimetric inequalities at given density levels and a way to iterate such inequalities. These tools are presented and apply to general metric measure measures. Our examples subsume the previous results of Mackay, Tyson, and Wildrick regarding non-self similar Sierpi'nski carpets, and extend them to many more general shapes as well as higher dimensions." @default.
- W3214377029 created "2021-11-22" @default.
- W3214377029 creator A5057207245 @default.
- W3214377029 creator A5080842792 @default.
- W3214377029 date "2021-11-15" @default.
- W3214377029 modified "2023-09-23" @default.
- W3214377029 title "Isoperimetric and Poincar'e inequalities on non-self-similar Sierpi'nski sponges: the borderline case" @default.
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- W3214377029 doi "https://doi.org/10.48550/arxiv.2111.07861" @default.
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