Geodesic
Radial extensions of bilipschitz maps between unit spheres
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 839-843

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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. 
@article{SEMR_2018_15_a130,
     author = {P. Alestalo and D. A. Trotsenko},
     title = {Radial extensions of bilipschitz maps between unit spheres},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {839--843},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a130/}
}
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P. Alestalo; D. A. Trotsenko. Radial extensions of bilipschitz maps between unit spheres. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 839-843. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a130/