Monge-Ampère and Hessian equations on compact Hermitian manifolds

Apparaît dans la collection : Complex Analytic and Differential Geometry

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.