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 \(A\subset E\).

Downloads

Published

2021-06-22

Issue

Vol. 46 No. 1 (2021)

Section

Articles

License

Copyright (c) 2021 The Finnish Mathematical Society

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite

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