题目：Convexity Estimate for the Homogeneous Complex Monge-Ampere Equation

报告人：胡京辰，中国科学院数学与系统科学研究院

时间：2023年12月5日（周二）16：00-16：50

地点：管理科研楼1418

摘要：In this talk, we will discuss the convexity of level sets of solutions to the homogenous complex Monge-Ampere(HCMA) equation in a ring-shaped domain with homogenous boundary conditions. The corresponding problems for the Laplace equation or more general quasi-linear equations have been studied by many experts; various techniques were developed, like constant rank theorems and the curvature estimates for the level sets. For the HCMA equation, to prove our result, we invented some new auxiliary functions, which make the computation more natural, and we also made use of the symmetry of the HCMA equation. We will also discuss its relation with the geodesics in the space of K\”ahler potentials, which are also governed by HCMA equations.