Publication

Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group

Martin Bauer, Martins Bruveris
Springer Verlag, 2013
Article
Résumé

We study Sobolev-type metrics of fractional order s a parts per thousand yen 0 on the group Diff (c) (M) of compactly supported diffeomorphisms of a manifold M. We show that for the important special case M = S (1), the geodesic distance on Diff (c) (S (1)) vanishes if and only if . For other manifolds, we obtain a partial characterization: the geodesic distance on Diff (c) (M) vanishes for and for , with N being a compact Riemannian manifold. On the other hand, the geodesic distance on Diff (c) (M) is positive for and dim(M) a parts per thousand yen 2, s a parts per thousand yen 1. For , we discuss the geodesic equations for these metrics. For n = 1, we obtain some well-known PDEs of hydrodynamics: Burgers' equation for s = 0, the modified Constantin-Lax-Majda equation for , and the Camassa-Holm equation for s = 1.

À propos de ce résultat
Cette page est générée automatiquement et peut contenir des informations qui ne sont pas correctes, complètes, à jour ou pertinentes par rapport à votre recherche. Il en va de même pour toutes les autres pages de ce site. Veillez à vérifier les informations auprès des sources officielles de l'EPFL.
Concepts associés

Chargement

Publications associées

Chargement