BIMSA > Complex Geometry Seminar Complex Geometry Seminar Continuity of Monge-Ampère Potentials on compact Hermitian manifolds
Continuity of Monge-Ampère Potentials on compact Hermitian manifolds
Organizers
Genglong Lin , Enric Sole Farre , Yingying Zhang
Speaker
Dang Quang Tuan
Time
Wednesday, April 8, 2026 2:00 PM - 3:30 PM
Venue
A3-4-101
Abstract
We prove a uniform estimate for the continuity of solutions to complex Monge--Ampère equations on compact Hermitian manifolds, using an auxiliary function method. As an application, we derive a uniform diameter bound for Hermitian metrics along the weak Chern--Ricci flow. Our approach also extends to the study of H\"older regularity of the least singular solution to the complex Monge--Ampère equation with a big reference form, as considered in [Boucksom, Guedj, Lu, {\it Peking Math J} (2025).]