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) Slawomir Dinew - Jagiellonian University,
Titre Complex Hessian equations on manifolds
Horaire14:00 à 15:00
RésumeGiven a C² smooth function u defined over a domain in C^n, the complex k-Hessian of u is the k^th symmetric sum S_k(u) of the eigenvalues of its Hessian matrix. The associated class of admissible functions is given by the conditions S_j(u) ≥ 0, j = 1, ⋯, k. These interpolate between subharmonic and plurisubharmonic functions. In the talk I will discuss the related potential theory and later I will focus on the solvability of the Dirichlet problem related to the k-Hessian equation in domains and on manifolds. In particular I will sketch an analogue of the Calabi-Yau theorem for these equations. If time permits some geometric applications will be mentioned.