几何分析讨论班

报告题目：Uniform estimates for complex Monge–Ampère equations: from local domains to big cohomology classes

报 告 人：周斌（北京大学）

时  间：2026年11月10日（星期二），下午15:00-16:00

地  点：海纳苑2幢204

摘  要：Complex Monge–Ampère equations are a central tool in complex geometry, and a priori estimates are essential to understanding their solutions. In this talk, I will trace the development of uniform estimates through three settings: the Dirichlet problem on bounded domains, equations on compact Kähler manifolds, and equations in big cohomology classes.

I will first explain how energy inequalities and iteration give estimates in the local setting. I will then discuss the compact Kähler case, where global geometry enters but the background form remains positive. Finally, I will consider big cohomology classes, where solutions may have unavoidable singularities. I will describe how auxiliary functions and quasi-plurisubharmonic envelopes help answer this question, and briefly mention related exponential integrability results.