The dual Minkowski problem for unbounded closed convex sets

Titie: The dual Minkowski problem for unbounded closed convex sets

Speaker: Deping Ye（Memorial University of Newfoundland）

Time: 2023-05-05 14:00-15:00

Location: 303, Building 2, Hainayuan, School of Mathematical Sciences, Zijingang Campus

Abstract: To find unknown convex body $K$ such that $\mu=\mathcal{M}(K, \cdot)$, where $\mu$ is a pregiven Borel measure on the unit sphere $S^{n-1}$ and $\mathcal{M}(K, \cdot)$ is a Borel measure on $S^{n-1}$ depending on $K$, is an important problem in convex geometry. Such a problem is called the Minkowski type problem and has found many applications in other areas, such as, partial differential equations, computer science, etc. Similar questions can be asked for unbounded convex sets, which are closely related to log-concave functions and convex hypersurfaces. These unbounded convex sets play important roles in analysis, probability, algebraic geometry, singularity theory, etc. In this talk, I will talk about some recent progress on these problems with concentration on a special case: the dual Minkowski problem for unbounded closed convex sets. I will discuss how to set up this problem and explain our existence of solutions to this problem.

Contact Person: LI qirui (qi-rui.li@zju.edu.cn)