A family of Monge-Ampère type operators converging to sigma_k, and their Minkowski problems
数学公众报告(120周年校庆系列第90场)
报告题目(Title)：A family of Monge-Ampère type operators converging to sigma_k, and their Minkowski problems
报告人(Speaker)：席东盟 副教授 (上海大学)
地点(Place)：后主楼1220
时间(Time)：2023年4月14日(周五), 10:00-11:00
邀请人(Inviter)：彦文娇
报告摘要
We introduced a new family of translation invariant geometric measures arising from Integral Geometry of convex bodies. These measures are related to a family of new Monge-Ampère type operators converging to a sigma_k operator. The Minkowski problems for these new measures are proposed and attacked. This is joint work with Erwin Lutwak, Deane Yang, and Gaoyong Zhang.
主讲人简介
席东盟，上海大学数学系副教授。主要研究凸几何与积分几何中的分析问题，尤其是在等周问题与几何测度的Minkowski问题取得了若干成果，包括：在积分几何中引入了并解决了一族平移不变几何测度的Minkowski问题，对应了一族收敛到sigma_k的Monge-Ampere型算子；解决了2维Dar猜想；建立了Orlicz Brunn-Minkowski不等式；得到了Gaussian概率空间中的Minkowski问题的正则解。相关成果被录用或发表在Comm. Pure Appl. Math.、J. Differential Geom.、Adv. Math.、Trans. Amer. Math. Soc.、J. Func. Anal.、Int. Math. Res. Not.等。
