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2 results on '"cat (0) metric spaces"'

1. Spectral Calculus and Lipschitz Extension for Barycentric Metric Spaces

Author

Mendel Manor and Naor Assaf

Subjects
markov cotype, lipschitz extension, cat (0) metric spaces, nonlinear spectral gaps, 54c20, 53c21, 46b85, Analysis, QA299.6-433
Abstract

The metric Markov cotype of barycentric metric spaces is computed, yielding the first class of metric spaces that are not Banach spaces for which this bi-Lipschitz invariant is understood. It is shown that this leads to new nonlinear spectral calculus inequalities, as well as a unified framework for Lipschitz extension, including new Lipschitz extension results for CAT (0) targets. An example that elucidates the relation between metric Markov cotype and Rademacher cotype is analyzed, showing that a classical Lipschitz extension theorem of Johnson, Lindenstrauss and Benyamini is asymptotically sharp.

Published
2013
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2. Spectral calculus and Lipschitz extension for barycentric metric spaces

Author

Assaf Naor and Manor Mendel

Subjects
Banach space, markov cotype, 54c20, Barycentric coordinate system, 01 natural sciences, 46b85, 010104 statistics & probability, Mathematics - Metric Geometry, Calculus, FOS: Mathematics, Mathematics::Metric Geometry, 0101 mathematics, Invariant (mathematics), Mathematics, QA299.6-433, Mathematics::Functional Analysis, cat (0) metric spaces, Markov chain, Applied Mathematics, 010102 general mathematics, lipschitz extension, Metric Geometry (math.MG), 53c21, Lipschitz continuity, Functional Analysis (math.FA), Mathematics - Functional Analysis, nonlinear spectral gaps, Nonlinear system, Metric space, Geometry and Topology, Analysis
Abstract

The metric Markov cotype of barycentric metric spaces is computed, yielding the first class of metric spaces that are not Banach spaces for which this bi-Lipschitz invariant is understood. It is shown that this leads to new nonlinear spectral calculus inequalities, as well as a unified framework for Lipschitz extension, including new Lipschitz extension results for CAT(0) targets. An example that elucidates the relation between metric Markov cotype and Rademacher cotype is analyzed, showing that a classical Lipschitz extension theorem of Johnson, Lindenstrauss and Benyamini is asymptotically sharp., Comment: referee comments addressed

Published
2013
Full Text
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