Abstract:

The dual Orlicz-Minkowski problem arises from modern convex geometry. In the smooth case, it is equivalent to solving a class of Monge-Ampere type equations defined on the unit hypersphere. These equations could be degenerate or singular in different conditions. We study some geometric flows related to the dual Orlicz-Minkowski problem. These flows involve Gauss curvature and functions of normal vectors and radial vectors. By proving their long-time existence and convergence, we obtain new existence results of solutions to the dual Orlicz-Minkowski problem for smooth measures. We also discuss the uniqueness and nonuniqueness of solutions to a planar case of this problem.

Speaker：

Jian Lu

2013年在清华大学获博士学位，现为华南师范大学副教授。研究方向主要为 Monge-Ampere 型等非线性偏微分方程及其应用。在数学学术期刊上发表论文十余篇，主持国家自然科学基金面上项目和优秀青年项目等多项课题。

Zoom:

https://us02web.zoom.us/j/82156646127?pwd=N1JSOStwcmV1dUdHanNSWkwzRGlhQT09

Passwords: 529643