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INICIO | 22 de febrero de 2024

Regular mappings between dimensions

Título inglés Regular mappings between dimensions
Título español Aplicaciones regulares entre dimensiones.
Autor/es David, Guy ; Semmes, Stephen
Organización Univ. París Sud Orsay, París, Francia
Revista 0214-1493
Publicación 2000, 44 (2): 369-417, 33 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés 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 λ: Rs → Rs−t and a subset E of B of substantial measure such that the pair (f, λ) is bilipschitz on E. We also compare these mappings in comparison with “nonlinear quotient mappings” from [6].
Clasificación UNESCO 121005
Palabras clave español Aplicación lipschitziana ; Espacio topológico regular ; Integrales singulares
Código MathReviews MR1800814
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Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)