Ressource pédagogique : F. Schulze - Mean curvature flow with generic initial data

cours / présentation - Date de création : 29-06-2021
Auteur(s) : Felix SCHULZE
Partagez !

Présentation de: F. Schulze - Mean curvature flow with generic initial data

Informations pratiques sur cette ressource

Langue du document : Anglais
Type pédagogique : cours / présentation
Niveau : doctorat
Durée d'exécution : 1 heure 1 minute 56 secondes
Contenu : image en mouvement
Document : video/mp4
Taille : 1.09 Go
Droits d'auteur : libre de droits, gratuit
Droits réservés à l'éditeur et aux auteurs. CC BY-NC-ND 4.0

Description de la ressource pédagogique

Description (résumé)

Mean curvature flow is the gradient flow of the area functional and constitutes a natural geometric heat equation on the space of hypersurfaces in an ambient Riemannian manifold. It is believed, similar to Ricci Flow in the intrinsic setting, to have the potential to serve as a tool to approach several fundamental conjectures in geometry. The obstacle for these applications is that the flow develops singularities, which one in general might not be able to classify completely. Nevertheless, a well-known conjecture of Huisken states that a generic mean curvature flow should have only spherical and cylindrical singularities. As a first step in this direction Colding-Minicozzi have shown in fundamental work that spheres and cylinders are the only linearly stable singularity models. As a second step toward Huisken's conjecture we show that mean curvature flow of generic initial closed surfaces in R^3 avoids asymptotically conical and non-spherical compact singularities. The main technical ingredient is a long-time existence and uniqueness result for ancient mean curvature flows that lie on one side of asymptotically conical or compact self-similarly shrinking solutions. This is joint work with Otis Chodosh, Kyeongsu Choi and Christos Mantoulidis.

"Domaine(s)" et indice(s) Dewey

  • Mathématiques (510)

Thème(s)

Intervenants, édition et diffusion

Intervenants

Fournisseur(s) de contenus : Fanny Bastien, Hugo BÉCHET

Diffusion

Document(s) annexe(s) - F. Schulze - Mean curvature flow with generic initial data

Partagez !

AUTEUR(S)

  • Felix SCHULZE

EN SAVOIR PLUS

  • Identifiant de la fiche
    63081
  • Identifiant
    oai:canal-u.fr:63081
  • Schéma de la métadonnée
  • Entrepôt d'origine
    Canal-U