Séminaires : Séminaire d'Analyse et Géométrie

Equipe(s) :
Responsables :O. Biquard, A. Deruelle, I. Itenberg, X. Ma
Email des responsables : {olivier.biquard, alix.deruelle, ilia.itenberg, xiaonan.ma}@imj-prg.fr
Salle : 15–25.502
Adresse :Jussieu

Orateur(s) Anda Degeratu - Universität Stuttgart,
Titre The Calabi Conjecture on QAC spaces
Horaire14:00 à 15:00
RésumeIn this talk we introduce the class of quasi-asymptotically conical (QAC) geometries, a less rigid Riemannian formulation of the QALE geometries introduced by Joyce in his study of crepant resolutions of Calabi-Yau orbifolds. Our set-up is in the category of real stratified spaces and Riemannian geometry. Given a QAC manifold, we identify the appropriate weighted Sobolev spaces, for which we prove the finite dimensionality of the null space for generalized Laplacians as well as their Fredholmness. We conclude with new examples of Ricci-flat Kähler metrics which have these type of asymptotic geometries. This talk is based on joint work with Rafe Mazzeo and with Ronan Conlon and Frederic Rochon.