中科院数学与系统科学研究院
数学研究所
中科院华罗庚数学重点实验室
华罗庚青年数学论坛
学术报告
报告人： 程经睿 博士（Stony Brook University）
题 目：A PDE approach to uniform and H\"older estimates for parabolic complex Monge-Ampere and Hessian equations
时 间：2022.03.11（星期五），09:00-11:00
地 点：腾讯会议：266-330-904
摘 要：We consider a new parabolic Monge-Ampere flow inspired from the parabolic Alexandrov maximum principle by Krylov-Tso. I will discuss various estimates and properties related to the new flow, including how the uniform and Holder estimates for complex Monge-Ampere can be generalized to the parabolic case using a PDE approach, and also that the flow converges to the complex Monge-Ampere as t tends to infinity.
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华罗庚青年数学论坛 学术报告2
报告人：程经睿 博士（Stony Brook University）
题 目：A gradient estimate for the complex Monge-Ampere equation
时 间：2022.03.18（星期五），09:00-11:00
地 点：腾讯会议：770-564-199
摘 要：I will explain how to estimate the L^p bound of the gradient of the solution to complex Monge-Ampere when the right hand side is non-degenerate and continuous. If one assumes Dini continuity of the right hand side, then the solution will be Lipschitz. If time permits, I will also explain how the idea can be applied to pseudo-Calabi flow, a flow whose stationary solution is csck (constant scalar curvature Kahler metric).
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