Rings and bilipschitz maps in Banach spaces

Författare

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

Nyckelord:

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 \(A\subset E\).

Nedladdningar

Publicerad

2021-06-22

Nummer

Vol 46 Nr 1 (2021)

Sektion

Articles

Licens

Copyright (c) 2021 The Finnish Mathematical Society

Creative Commons-licens

Detta verk är licensierat under en Creative Commons Erkännande-IckeKommersiell 4.0 Internationell-licens.

Referera så här

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