Stability of strongly Lipschitz contractible balls in Alexandrov spaces

Ayato Mitsuishi, Takao Yamaguchi

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Recently, we proved that every finite dimensional Alexandrov space is strongly locally Lipschitz contractible. In the present paper, we consider the set M of all isometry classes of Alexandrov spaces of curvature≥ –1 and of fixed dimension having upper diameter bound and lower volume bound, and prove that there exists a constant N depending on the parameters determining M such that every space in M can be covered by at most N strongly Lipschitz contractible balls. Also, we prove that there exists a constant N′ depending on M such that every space in M can be covered by at most N′ strongly Lipschitz contractible and convex regions.

Original languageEnglish
Pages (from-to)995-1009
Number of pages15
JournalMathematische Zeitschrift
Volume277
Issue number3-4
DOIs
Publication statusPublished - 2014

ASJC Scopus subject areas

  • Mathematics(all)

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