EVENT DETAILS AND ABSTRACT

Title: Weak solutions of complex Hessian equations on compact Hermitian manifolds
Speaker: Slawomir Kolodziej
Speaker Info: Jagiellonian University
Brief Description:
Special Note:
Abstract:

This is joint work with Cuong Ngoc Nguyen. Let (X,ω) be a compact Hermitian manifold of complex dimension n. We prove the existence of weak solutions to the complex Hessian equation

(ω + dd^cφ)^k∧ω^n-k = cfωⁿ,

where 0≤f∈ L^p(X,ωⁿ), p> n/k, and u so called (ω, k) subharmonic function. For smooth, positive data the equation has recently been solved by Szekelyhidi and Zhang. We also obtain stability estimates for weak solutions.