Some remarks about metric spaces, spherical mappings, functions and their derivatives.

Título inglés Some remarks about metric spaces, spherical mappings, functions and their derivatives.
Título español Algunos comentarios sobre espacios métricos, mapeos esféricos, funciones y sus derivadas.
Autor/es Semmes, Stephen
Organización Dep. Math. Rice Univ., Houston (Texas), Estados Unidos
Revista 0214-1493
Publicación 1996, 40 (2): 411-430, 12 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés If p Î Rn, then we have the radial projection map from Rn {p} onto a sphere. Sometimes one can construct similar mappings on metric spaces even when the space is nontrivially different from Euclidean space, so that the existence of such a mapping becomes a sign of approximately Euclidean geometry. The existence of such spherical mappings can be used to derive estimates for the values of a function in terms of its gradient, which can then be used to derive Sobolev inequalities, etc. In this paper we shall discuss these topics mostly in the context of metric doubling measures, which provides a nontrivial setting in which these mappings exist and can be used. This provides an alternative approach (or understanding) of the results in [DS], and a variation on the themes of [Se4].
Clasificación UNESCO 120225 ; 121003
Palabras clave español Espacios métricos ; Análisis funcional ; Funciones de variable compleja ; Función derivada ; Geometría euclídea ; Desigualdades ; Formas diferenciales ; Medidas de Borel
Código MathReviews MR1425628
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