关于举行胡京辰副研究员（四川大学）学术报告会的通知

报告主题:  Convexity Estimates for Solutions to Monge-Ampere Equations

报 告 人:  胡京辰 副研究员 

报告时间： 2026年4月9日（星期四）下午3:30-4:30

报告地点： 37号楼3A02室

邀 请 人:  袁日荣

欢迎广大师生前往！

数学学院

2026年4月6日

  报告摘要：

  In previous work, we identify some algebraic relations which leads to interesting estimates for complex Monge-Ampere equations. In this talk, we present some applications of this technique.

  1. We prove that the potential function of a Kahler-Einstein metric in a convex domain is convex;

  2. We prove that the soltution of the non-degenerate complex Monge-Ampere equation $\det(u_{I\overline j})=1$ in a convex domain is power convex;

  3. We prove that the solution of the homogenous complex Monge-Ampere equation in a convex ring is exponential convex.

  In addition, we discuss some possible further applications of this technique.    

  报告人介绍：

  胡京辰，四川大学特聘副研究员，2018 年毕业于中国科学技术大学，获博士学位。主要研究领域为偏微分方程与几何分析，在 Math Ann、CVPDE、JFA、IMRN等著名期刊发表文章近 10 篇。