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- W3093896268 abstract "We study the infimal value of the Hausdorff dimension of spaces that are Holder equivalent to a given metric space; we call this bi-Holder-invariant Holder dimension. This definition and some of our methods are analogous to those used in the study of conformal dimension. We prove that Holder dimension is bounded above by capacity dimension for compact, doubling metric spaces. As a corollary, we obtain that Holder dimension is equal to topological dimension for compact, locally self-similar metric spaces. In the process, we show that any compact, doubling metric space can be mapped into Hilbert space so that the map is a bi-Holder homeomorphism onto its image and the Hausdorff dimension of the image is arbitrarily close to the original space's capacity dimension. We provide examples to illustrate the sharpness of our results. For instance, one example shows Holder dimension can be strictly greater than topological dimension for non-self-similar spaces, and another shows the Holder dimension need not be attained." @default.
- W3093896268 created "2020-10-29" @default.
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- W3093896268 date "2020-10-20" @default.
- W3093896268 modified "2023-10-17" @default.
- W3093896268 title "Minimising Hausdorff dimension under Hölder equivalence" @default.
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- W3093896268 doi "https://doi.org/10.1112/jlms.12391" @default.
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