Growth rate of Lipschitz constants for retractions between finite subset spaces

Earnest Akofor, Leonid V. Kovalev

Research output: Contribution to journalArticlepeer-review

Abstract

For any metric space X, finite subset spaces of X provide a sequence of isometric embeddings X = X(1) ⊂ X(2) ⊂ · · ·. The existence of Lipschitz retractions rn : X(n) → X(n-1) depends on the geometry of X in a subtle way. Such retractions are known to exist when X is an Hadamard space or a finite-dimensional normed space. But even in these cases it was unknown whether the sequence {rn} can be uniformly Lipschitz. We give a negative answer by proving that Lip(rn) must grow with n when X is a normed space or an Hadamard space.

Original languageEnglish (US)
Pages (from-to)317-326
Number of pages10
JournalStudia Mathematica
Volume260
Issue number3
DOIs
StatePublished - 2021

Keywords

  • Finite subset space
  • Hadamard space
  • Lipschitz retraction
  • Metric space
  • Normed space

ASJC Scopus subject areas

  • Mathematics(all)

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