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JOURNALS // Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports] // Archive

Sib. Èlektron. Mat. Izv., 2018 Volume 15, Pages 839–843 (Mi semr958)

This article is cited in 1 paper

Real, complex and functional analysis

Radial extensions of bilipschitz maps between unit spheres

P. Alestaloa, D. A. Trotsenkob

a Department of Mathematics and Systems Analysis, Aalto University, PL 11100 Aalto, Helsinki, Finland
b Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia

Abstract: Let $E_1$ and $E_2$ be real inner product spaces, and let $S_1$ and $S_2$ be the corresponding unit spheres. We consider different proofs showing that the radial extension of an $L$-bilipschitz map $f\colon S_1\to S_2$ is $L$-bilipschitz with the same constant $L$. We also consider certain other sets having this kind of an extension property.

Keywords: bilipschitz map, unit sphere.

UDC: 517.548

MSC: 30C65

Received December 18, 2017, published August 6, 2018

Language: English

DOI: 10.17377/semi.2018.15.071



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