Spectral calculus and Lipschitz extension for barycentric metric spaces

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.

referee comments addressed

References in corpus (5)

• Nonlinear spectral calculus and super-expanders
• Expanders with respect to Hadamard spaces and random graphs
• Nagata dimension, quasisymmetric embeddings, and Lipschitz extensions
• An introduction to the Ribe program
• Metric Extension Operators, Vertex Sparsifiers and Lipschitz Extendability

Cited by in corpus (10)

• Nonlinear spectral calculus and super-expanders
• Expanders with respect to Hadamard spaces and random graphs
• Extending and improving conical bicombings
• An average John theorem
• Nonpositive curvature is not coarsely universal
• Absolute Lipschitz extendability and linear projection constants
• Ergodic theorem in Hadamard spaces in terms of inductive means
• A non-compact convex hull in generalized non-positive curvature
• Metric $X_p$ inequalities
• Markov Type constants, flat tori and Wasserstein spaces