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Regular mappings between dimensions
David, Guy
Semmes, Stephen

Data: 2000
Resum: The notions of Lipschitz and bilipschitz mappings provide classes of mappings connected to the geometry of metric spaces in certain ways. A notion between these two is given by "regular mappings" (reviewed in Section 1), in which some non-bilipschitz behavior is allowed, but with limitations on this, and in a quantitative way. In this paper we look at a class of mappings called (s, t)-regular mappings. These mappings are the same as ordinary regular mappings when s = t, but otherwise they behave somewhat like projections. In particular, they can map sets with Hausdorff dimension s to sets of Hausdorff dimension t. We mostly consider the case of mappings between Euclidean spaces, and show in particular that if f : Rs --> Rn is an (s, t)-regular mapping, then for each ball B in Rs there is a linear mapping [lambda] : Rs --> Rs-t and a subset E of B of substantial measure such that the pair (f, [lambda]) is bilipschitz on E. We also compare these mappings in comparison with "nonlinear quotient mappings" from [6].
Drets: Tots els drets reservats.
Llengua: Anglès
Document: Article ; recerca ; Versió publicada
Publicat a: Publicacions matemàtiques, V. 44 N. 2 (2000) , p. 369-417, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/37993
DOI: 10.5565/PUBLMAT_44200_02

49 p, 306.8 KB

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