Rings and bilipschitz maps in Banach spaces

Authors

  • Pekka Tukia University of Helsinki, Department of Mathematics and Statistics
  • Jussi Väisälä University of Helsinki, Department of Mathematics and Statistics

Keywords:

Ring, bilipschitz, normed space, geometric modulus

Abstract

We define the geometric modulus \(GM(A)\) of a ring \(A\) in a normed space \(E\) and show that a set-bounded homeomorphism \(f\colon E\to E\) is bilipschitz if and only if \(|GM(A)-GM(fA)|\le c\) for all rings \(A\subset E\).
Issue
Vol. 46 No. 1 (2021)
Section
Articles

Published

2021-06-22

How to Cite

Tukia, P., & Väisälä, J. (2021). Rings and bilipschitz maps in Banach spaces. Annales Fennici Mathematici, 46(1), 587–591. Retrieved from https://afm.journal.fi/article/view/109693

Copyright (c) 2021 The Finnish Mathematical Society

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