Bi-Lipschitz Decomposition of Lipschitz functions into a Metric space
| dc.creator | Schul, Raanan | |
| dc.date | 2007-02-22 | |
| dc.date | 2008-06-12 | |
| dc.date.accessioned | 2026-07-07T09:44:03Z | |
| dc.date.available | 2026-07-07T09:44:03Z | |
| dc.description | We prove a quantitative version of the following statement. Given a Lipschitz function f from the k-dimensional unit cube into a general metric space, one can decomposed f into a finite number of BiLipschitz functions f|_{F_i} so that the k-Hausdorff content of f([0,1]^k\setminus \cup F_i) is small. We thus generalize a theorem of P. Jones (1988) from the setting of R^d to the setting of a general metric space. This positively answers problem 11.13 in ``Fractured Fractals and Broken Dreams" by G. David and S. Semmes, or equivalently, question 9 from ``Thirty-three yes or no questions about mappings, measures, and metrics" by J. Heinonen and S. Semmes. Our statements extend to the case of {\it coarse} Lipschitz functions. | |
| dc.description | 11 pages. no figures. Paragraph surveying history has been corrected after referee report! | |
| dc.identifier | https://arxiv.org/abs/math/0702630 | |
| dc.identifier | http://arxiv.org/abs/math/0702630 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162731 | |
| dc.subject | Metric Geometry | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 28a75 | |
| dc.title | Bi-Lipschitz Decomposition of Lipschitz functions into a Metric space | |
| dc.type | text |