The dual Minkowski problem for unbounded closed convex sets

Speaker: YE Deping (Memorial University of Newfoundland)

Venue: 303, Building 2, Haina Court, 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 areassuch aspartial 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 upthis problem and explain ourexistence of solutions to this problem.

Professor Deping Ye received his bachelor's degree from Shandong University in 2000 and studied as a master's degree in Zhejiang University from 2000 to 2003. In 2009, he graduated from Case Western Reserve University in the United States and now works at Memorial Canada University of Newfoundland, and chairs the National Natural Science Foundation of Canada (NSERC). He received the JMAA Ames Award in 2017. His research interests include convex geometry analysis, geometric and functional inequalities, stochastic matrices, quantum information theory, and statistics. It has been published in the internationally renowned journal J.unct.Anal., Calc. Var. Partial Differential Equations,Adv. Math., Comm. Pure Appl. Math., Math. Ann., He has published nearly 40 papers.