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) Hans-Joachim Hein - University of Munster,
Titre Kähler-Einstein metrics on complex hyperbolic cusps and degenerations of surfaces of general type
Horaire14:00 à 15:00
RésumeA complex hyperbolic cusp is an end of a finite-volume quotient of complex hyperbolic space. Up to a finite cover, any such cusp can be realized as the punctured unit disk bundle of a negative line bundle over an abelian variety. The Dirichlet problem for complete Kähler-Einstein metrics on this space with boundary data prescribed on the unit circle bundle is well-posed. We determine the precise asymptotics of its solutions towards the zero section. I will also explain an application to the geometry of degenerating Kähler-Einstein metrics on surfaces of general type via gluing. This is joint work with Xin Fu and Xumin Jiang.