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- W4300167977 abstract "A well-known class of questions asks the following: If $X$ and $Y$ are metric measure spaces and $f:Xrightarrow Y$ is a Lipschitz mapping whose image has positive measure, then must $f$ have large pieces on which it is bi-Lipschitz? Building on methods of David (who is not the present author) and Semmes, we answer this question in the affirmative for Lipschitz mappings between certain types of Ahlfors $s$-regular, topological $d$-manifolds. In general, these manifolds need not be bi-Lipschitz embeddable in any Euclidean space. To prove the result, we use some facts on the Gromov-Hausdorff convergence of manifolds and a topological theorem of Bonk and Kleiner. This also yields a new proof of the uniform rectifiability of some metric manifolds." @default.
- W4300167977 created "2022-10-03" @default.
- W4300167977 creator A5007055272 @default.
- W4300167977 date "2013-12-13" @default.
- W4300167977 modified "2023-10-16" @default.
- W4300167977 title "Bi-Lipschitz Pieces between Manifolds" @default.
- W4300167977 doi "https://doi.org/10.48550/arxiv.1312.3911" @default.
- W4300167977 hasPublicationYear "2013" @default.
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