Lipschitz Clustering in Metric Spaces

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, the Lipschitz clustering property of a metric space refers to the existence of Lipschitz retractions between its finite subset spaces. Obstructions to this property can be either topological or geometric features of the space. We prove that uniformly disconnected spaces have the Lipschitz clustering property, while for some connected spaces, the lack of sufficiently short connecting curves turns out to be an obstruction. This property is shown to be invariant under quasihomogeneous maps, but not under quasisymmetric ones.

Original languageEnglish (US)
Article number188
JournalJournal of Geometric Analysis
Volume32
Issue number7
DOIs
StatePublished - Jul 2022

Keywords

  • Clustering
  • Finite subset space
  • Lipschitz retraction
  • Metric space
  • Ultrametric

ASJC Scopus subject areas

  • Geometry and Topology

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