Plongements lipschitziens dans Rn

By P. Assouad. 2003

364 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/eefb25d7b29c1ae94496406b17aea1acbd9873af

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Citations in the corpus

Navigating nets: simple algorithms for proximity search (2004, background): “Our flrst contribution is conceptual|we put forward (in the context of NNS) a natural notion of abstract dimension, which is based on one of Assouad [ Ass83 ] (from the theory of analysis on metric spaces).”
Markov chains in smooth Banach spaces and Gromov hyperbolic metric spaces (2004, background): “It may be replaced with any probability space equivalent to [0, 1].”
Dimensions, Whitney covers, and tubular neighborhoods (2012, methodology): “ical) neighborhoods of a given set. In this respect, also the role of geometrical conditions, such as porosity and uniform perfectness, is examined. Our study continues and combines e.g. the works of [1, 2, 3, 5, 17, 24, 25, 27, 32, 40]. A common theme to most of our results is that we explore means”
Harmonic analysis, cohomology, and the large-scale geometry of amenable groups (2004, result): “It is a highly non-trivial fact that the converse is also true, a result which follows from Assouad's "doubling theorem" [ 1 ] (we thank Mario Bonk and Bruce Kleiner for the information concerning Assouad's result).”
Lp compression, traveling salesmen, and stable walks (2009, unknown): “Hence, dLG(Z) ( ( f , x), (g, y) )pα (12) = TSP(A; x, y)pα (15) .”
Assouad's theorem with dimension independent of the snowflaking (2010, methodology): “embedding of H1,d 1−ε N0 from Theorem 1.3. This would yield the bound cRN H1,d 1−ε N0 √ ε 6 D. 1.2. Previous work and an overview of the proof of Theorem 1.2. The classical proof of Assouad’s theorem [4, 15] yields the dimension bound N(K,ε) 6 c(K)/εO(1). In [13] Gupta-Krauthgamer-Lee announced a si”
Embedding of hyperbolic groups into products of binary trees (2007, result): “The result should be compared with the Bonk–Schramm embedding theorem [BoS], which uses the Assouad embedding result [ As1 ].”