勷勤数学•专家报告

题      目：Recent progress on the Monge-Ampere (hyperplane) obstacle problem

报  告  人：涂绪山 博士  (邀请人：鲁建)

                                   香港科技大学

时      间：1月3日  10：00-11：00

地     点：数科院西楼111

报告人简介:

       涂绪山，博士，现为香港科技大学博士后。本科、直博毕业于清华大学。研究领域主要集中在 Monge-Ampère 型非线性椭圆偏微分方程及其应用，特别关注其对应的椭圆理论，包括边界正则性、强极值原理、ABP 估计，以及奇点和障碍问题等。

摘      要：

       In this talk, we explore refined Alexandrov-Bakelman-Pucci (ABP) estimates for convex solutions, highlighting how solutions to the Monge-Ampere obstacle problems and Monge-Ampere isolated singularity problems act as extremal configurations in a specific context. We then discuss recent and significant theoretical advancements related to these problems and extend these findings to a Monge-Ampère type obstacle problem derived from the Lp Minkowski problem for p in [1, n+1) with an emphasis on the regularity and classification of solutions. This research is conducted in collaboration with Tianling Jin and Jingang Xiong.

          欢迎老师、同学们参加、交流！