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

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.

Funding Agency Grant Number
Academy of Finland
The work was supported by the Academy of Finland and the Sobolev Institute of Mathematics.


DOI: https://doi.org/10.17377/semi.2018.15.071

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Bibliographic databases:

Document Type: Article
UDC: 517.548
MSC: 30C65
Received December 18, 2017, published August 6, 2018
Language: English

Citation: P. Alestalo, D. A. Trotsenko, “Radial extensions of bilipschitz maps between unit spheres”, Sib. Èlektron. Mat. Izv., 15 (2018), 839–843

Citation in format AMSBIB
\Bibitem{AleTro18}
\by P.~Alestalo, D.~A.~Trotsenko
\paper Radial extensions of bilipschitz maps between unit spheres
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 839--843
\mathnet{http://mi.mathnet.ru/semr958}
\crossref{https://doi.org/10.17377/semi.2018.15.071}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000454860200012}


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