Title：Characterizations of convex functions and monotone vector fields on metric measure space
Speaker：韩邦先（University of Bonn）
Time：2017年12月20日（周三）   下午15:00-16:00
Room：东区管理科研楼  数学科学学院1518室
 
Abstract： There are two main aims of this work. The first aim is to characterize the convexity of functions on metric measure space, so that we could link the existence of some special K-convex functions to the particular metric structure of the space, which is a new approach to deal with some rigidity theorems such as /splitting theorem" and /volume cone implies metric cone theorem". The second aim is to study the convexity/monotonicity of non-smooth vector fields on metric measure space. We introduce the notion of K-monotonicity which is stable under measured Gromov-Hausdorff convergence, then characterize the K-monotone vector fields in several equivalent ways.