Extending Lipschitz functions via random metric partitions

By James R. Lee, Assaf Naor. 2005

174 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/715fd8b59faa5438102f1eeb834d3155d64c6073

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In Computational Theory and Mathematics

In Discrete Mathematics and Combinatorics

Citations in the corpus

Vector‐valued optimal Lipschitz extensions (2010, background): “We remark that the general problem of finding Lipschitz extensions of a Lipschitz function from a subset Y of a metric space X to another metric space Z has been thoroughly studied, with diverse applications in mathematics, computer science, and engineering (see the books [20, 3], as well as the int”
Poincaré inequalities, embeddings, and wild groups (2010, methodology): “We note that in the extension theorems we quote below from [26] the role of the target space being a Banach space is very weak, and it can also be, for example, any CAT(0) space; we refer to [26] for a discussion of this issue.”
Metric Spaces with Linear Extensions Preserving Lipschitz Condition (2004, methodology): “Remark 2.22 The last inequality can be easily derived from Theorem 1.4 of the paper [ LN ] by Lee and Naor on “absolute” Lipschitz extendability of doubling metric spaces.4 Their proof is based on a probabilistic argument.”
Comparison of Metric Spectral Gaps (2013, background): “The case of compact Riemannian surfaces is due to [62], with subsequent improved bounds on ε(X; δ) > 0 obtained in [63].”
Lectures on Lipschitz analysis (2005, unknown): “References to the topics advertized in this introduction include [18], [50], [17], [80], [20], [59], [16], [25], [63], [5], [67], [64], [47], [73], [62], [43].”
Approximation properties and Schauder decompositions in Lipschitz-free spaces (2012, methodology): “However, adapting a theorem of Kislyakov [8], Naor and 2010 Mathematics Subject Classification.”
Markov chains in smooth Banach spaces and Gromov hyperbolic metric spaces (2004, background): “We refer to [65, 6, 41 ] and the references therein for an account of known results on Lipschitz extension.”
Products of Lipschitz-free spaces and applications (2014, background): “It involves a construction by Lee and Naor from [12], and the fact that R admits a so-called K-gentle partition of the unity with respect to F , which in turn induces the mentioned extension E.”