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 |
Acceso al artículo completo |