数学学院（珠海）五周年院庆系列学术报告（一）：Geometric analysis on metric spaces

讲座时间 Datetime: 

星期三, 2020/09/30 - 从 16:30 到 17:30

地点 Venue: 

海琴2号A457会议室

报告人 Speaker: 

朱熹平 教授

单位 Affiliation: 

中山大学

报告摘要 Abstract: 

The concept of generalized sectional curvature (or generalized Ricci curvature, respectively) was successfully extended to certain metric spaces by Alexandrov (or Lott-Sturm-Villani, respectively). In this talk we discuss certain elliptic type partial differential equations on these metric spaces to reveal the relations among the solutions and the geometry of the metric spaces. We will first show the compatibility of Alexandrov curvature and Lott-Sturm-Villani curvature. Next, we will consider the Laplacian equation and heat equation on metric spaces. In particular, we will obtain the asymptotic behaviors of the eigenvalues. In the last part, we will show the regularity and quantitative gradient estimates for harmonic maps on metric spaces. This talk is based on several joint works with Hui-Chun Zhang and Xiao Zhong.