S. Kolodziej - Monge-Ampère and Hessian equations on compact Hermitian manifolds

Slawomir Kolodziej (1) , Jérémy Magnien (2)

1 Faculty of Mathematics and Computer Science of the Jagiellonian University
2 IF - Institut Fourier

Let (X, ω) be a compact Hermitian manifold of complex dimension n. I shall discuss some recent results concerning weak solutions to the complex Monge-Ampère equation and, the more general, complex Hessian equation (ω+ddc φ)k∧ωn−k =cfωn,(where 0≤f belongs to some Lp space) including existence, stability and H ̈older continuity. They were obtained in collaboration with S lawomir Dinew and Cuong Ngoc Nguyen. I would like to high- light interesting open problems.

Mots clés: Complex analytic and differential geometry 2017; Grenoble; Monge-Ampère; Hessian; equations; Hermitian manifolds; https://www.canal-u.tv/video/institut_fourier/s_kolodziej_monge_ampere_and_hessian_equations_on_compact_hermitian_manifolds.39669

Domaines: Géométrie différentielle [math.DG]

Slawomir Kolodziej, Jérémy Magnien. S. Kolodziej - Monge-Ampère and Hessian equations on compact Hermitian manifolds: Complex analytic and differential geometry 2017. 2017. ⟨medihal-01615497⟩