On the nonexistence of bilipschitz parametrizations and geometric problems about A-weights.

Título inglés On the nonexistence of bilipschitz parametrizations and geometric problems about A-weights.
Título español Inexistencia de parametrizaciones bilipschitzianas y problemas geométricos alrededor de pesos A.
Autor/es Semmes, Stephen
Organización Dep. Math. Rice Univ., Houston (Texas), Estados Unidos;IHES, Bures-sur-Yvette, Francia
Revista 0213-2230
Publicación 1996, 12 (2): 337-410, 45 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés How can one recognize when a metric space is bilipschitz equivalent to an Euclidean space? One should not take the abstraction of metric spaces too seriously here; subsets of Rn are already quite interesting. It is easy to generate geometric conditions which are necessary for bilipschitz equivalence, but it is not clear that such conditions should ever be sufficient. The main point of this paper is that the optimistic conjectures about the existence of bilipschitz parametrizations are wrong. In other words, there are spaces whose geometry is very similar to but still distinct from Euclidean geometry. Related questions of bilipschitz equivalence and embeddings are addressed for metric spaces obtained by deforming the Euclidean metric on Rn using an A weight.
Clasificación UNESCO 120210 ; 120404
Palabras clave español Aplicación Lipschitziana ; Espacios métricos ; Variedades topológicas ; Espacio euclídeo ; Equivalencias geométricas ; Parametrización
Código MathReviews MR1402671
Código Z-Math Zbl 0858.46017
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