讲座题目：A class of optimal transportation problems on the sphere

主办单位：三峡数学研究中心/理学院

报告专家：李奇睿 研究员 （浙江大学）

报告时间：2024年6月24日（星期一）上午9:00-11:00

报告地点：腾讯会议：360 731 699

报告摘要：In this talk, we discuss a class of optimal transport problems on the sphere, with cost function $c(x,y)=F(d(x,y))$, where d is the spherical distance. We allow that F is a smooth function defined only in a subinterval of $[0,\pi]$, while c takes $-\infty$ at where F is not defined. Under suitable conditions, we show there is an optimal map solving the problem. In particular, if $F(d)=\log (\kappa \cos d -1)$ with $\kappa>1$, or $F(d)=\log\cos d$, then the associated optimal transport problem is respectively equivalent to the refractor problem in reshaping light beams, or the Aleksandrov problem for hypersurfaces with prescribed curvature.

报告人简介：李奇睿，浙江大学数学科学学院研究员，博士生导师。研究方向是几何分析与完全非线性方程。近年来与合作者在Monge最优运输问题，预定曲率问题，几何流等方向取得若干成果，在 J. Eur. Math. Soc.， J. Differential Geom.，Adv. Math.，Arch. Rat. Mech. Anal., Trans. Amer. Math. Soc.等著名期刊上发表多篇学术论文。