Monge-Ampère and Hessian equations on compact Hermitian manifolds

Hessian
grenoble
Complex analytic and differential geometry 2017
[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]
Monge-Ampère
equations
Hermitian manifolds
https://www.canal-u.tv/video/institut_fourier/s_kolodziej_monge_ampere_and_hessian_equations_on_compact_hermitian_manifolds.39669

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.

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Monge-Ampère and Hessian equations on compact Hermitian manifolds

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Monge-Ampère and Hessian equations on compact Hermitian manifolds

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