Rings and bilipschitz maps in Banach spaces

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 \(A\subset E\).