Abstract: On a compact Hermitian manifold X we consider the complex Monge-Ampère equation with right-hand side f in L^p, p>1 and semipositive and big reference form omgea. We prove that there is a continuous solution which is smooth in a Zariski open set if an additional regularity assumption on the density f is assumed. As an application, we obtain a singular Hermitian analogue of Yau’s solution to the Calabi conjecture. This is a joint work with Vincent Guedj announced on arXiv:2107.01938.
Speaker：Hoang-Chinh Lu
Dr. Hoang-Chinh Lu is an assistant professor at University Paris-Saclay. He is working on complex geometry and pluripotential theory with focus on canonical metrics, Monge-Ampère equations, geometric flows.
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