Metric Sobolev spaces
Koskela, Pekka
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We describe an approach to establish a theory of metric Sobolev spaces based on Lipschitz functions and their pointwise Lipschitz constants and the Poincaré inequality.
Displaying similar documents to “Characterizations of snowflake metric spaces.”
Metric Sobolev spaces
Bi-Lipschitz embeddings into low-dimensional Euclidean spaces
Jiří Matoušek (1990)
Commentationes Mathematicae Universitatis Carolinae
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On some properties of hyperconvex spaces.
Borkowski, Marcin, Bugajewski, Dariusz, Phulara, Dev (2010)
Fixed Point Theory and Applications [electronic only]
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On relations among metric derived numbers
Martin Koc (2009)
Acta Universitatis Carolinae. Mathematica et Physica
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On the Lifshits Constant for Hyperspaces
K. Leśniak (2007)
Bulletin of the Polish Academy of Sciences. Mathematics
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The Lifshits theorem states that any k-uniformly Lipschitz map with a bounded orbit on a complete metric space X has a fixed point provided k < ϰ(X) where ϰ(X) is the so-called Lifshits constant of X. For many spaces we have ϰ(X) > 1. It is interesting whether we can use the Lifshits theorem in the theory of iterated function systems. Therefore we investigate the value of the Lifshits constant for several classes of hyperspaces.
Isometry groups of non standard metric products
Bogdana Oliynyk (2013)
Open Mathematics
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We consider isometry groups of a fairly general class of non standard products of metric spaces. We present sufficient conditions under which the isometry group of a non standard product of metric spaces splits as a permutation group into direct or wreath product of isometry groups of some metric spaces.
Upper sets and quasisymmetric maps.
Trotsenko, D.A., Väisälä, J. (1999)
Annales Academiae Scientiarum Fennicae. Mathematica
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On the nonexistence of bilipschitz parametrizations and geometric problems about A-weights.
Stephen Semmes (1996)
Revista Matemática Iberoamericana
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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 R 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...