一、报告题目：A class of optimal transportation problems on the sphere
二、报告人：李奇睿教授
三、时间：2024年6月10日(周一)下午15:00-16:00
四、地点：闻理园A4-309
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。研究方向是完全非线性方程与几何分析。近年来与合作者在Monge最优运输问题，预定曲率问题，几何流等方向取得丰富成果，已在J. Eur. Math. Soc.，J. Differential Geom.，Adv. Math.，J. Funct. Anal.，Trans. Amer. Math. Soc.等国际著名期刊上发表论文近30篇。
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