Geodesic completeness of the $H^{3/2}$ metric on $\mathrm{Diff}(S^{1})$ - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Monatshefte für Mathematik Année : 2020

Geodesic completeness of the $H^{3/2}$ metric on $\mathrm{Diff}(S^{1})$

Boris Kolev
Stephen C. Preston
  • Fonction : Auteur
  • PersonId : 970559

Résumé

Of concern is the study of the long-time existence of solutions to the Euler--Arnold equation of the right-invariant $H^{3/2}$-metric on the diffeomorphism group of the circle. In previous work by Escher and Kolev it has been shown that this equation admits long-time solutions if the order $s$ of the metric is greater than $3/2$, the behaviour for the critical Sobolev index $s=3/2$ has been left open. In this article we fill this gap by proving the analogous result also for the boundary case. The behaviour of the $H^{3/2}$-metric is, however, still different from its higher order counter parts, as it does not induce a complete Riemannian metric on any group of Sobolev diffeomorphisms.
Fichier principal
Vignette du fichier
BKP2020.pdf (161.52 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02112529 , version 1 (26-04-2019)
hal-02112529 , version 2 (06-11-2019)
hal-02112529 , version 3 (13-03-2020)

Identifiants

Citer

Martin Bauer, Boris Kolev, Stephen C. Preston. Geodesic completeness of the $H^{3/2}$ metric on $\mathrm{Diff}(S^{1})$. Monatshefte für Mathematik, 2020, 193 (2), pp.233 - 245. ⟨10.1007/s00605-020-01405-8⟩. ⟨hal-02112529v3⟩
98 Consultations
109 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More