Comptes Rendus
no. 11
Geometry/Functional Analysis
Absolute Lipschitz extendability
[Sur la propriété d'extension lipschitzienne absolue]

Présenté par : Michael Gromov

James R. Lee1 ; Assar Naor2
1 Computer Science Division, University of California at Berkeley, Berkeley, CA 94720, USA
2 Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA
Comptes Rendus. Mathématique, Volume 338 (2004) no. 11, pp. 859-862.

On dit qu'un espace métrique X a la propriété d'extension lipschitzienne absolue si pour tout espace de Banach Z, toute fonction lipschitzienne f de X dans Z peut être étendue à tout espace métrique Y contenant X, avec une perte dans la constante de Lipschitz de l'extension qui ne dépend pas du choix de Y,Z et f. Nous montrons que plusieurs classes naturelles d'espaces métriques ont la propriété d'extension lipschitzienne absolue.

A metric space X is said to be absolutely Lipschitz extendable if every Lipschitz function f from X into any Banach space Z can be extended to any containing space Y⊇X, where the loss in the Lipschitz constant in the extension is independent of Y,Z, and f. We show that various classes of natural metric spaces are absolutely Lipschitz extendable.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.03.005
James R. Lee 1 ; Assar Naor 2

1 Computer Science Division, University of California at Berkeley, Berkeley, CA 94720, USA
2 Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA 
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James R. Lee; Assar Naor. Absolute Lipschitz extendability. Comptes Rendus. Mathématique, Volume 338 (2004) no. 11, pp. 859-862. doi : 10.1016/j.crma.2004.03.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.03.005/

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