Geodesic
Rings and bilipschitz maps in Banach spaces
Pekka Tukia1 ; Jussi Väisälä1
1University of Helsinki, Department of Mathematics and Statistics
Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 587-591
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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 $A\subset E$.
Keywords: Ring, bilipschitz, normed space, geometric modulus

Pekka Tukia  1   ; Jussi Väisälä  1

1 University of Helsinki, Department of Mathematics and Statistics 
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Pekka Tukia; Jussi Väisälä. Rings and bilipschitz maps in Banach spaces. Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 587-591. http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a35/