37000gcom威尼斯 2022年 第16期 数理大讲堂 暨“喜迎90周年校庆”系列讲座 第13期

报告人：熊革教授（同济大学）

报告时间：2022年12月20日14：00-15：00

腾讯会议：281-771-646

题目：The plane logarithmic Minkowski problem

摘要：

    The classical Minkowski’s existence theorem due to Minkowski and Aleksandrov characterizes the surface area measure   of a convex body  in   More precisely, it solves the Monge-Ampere equation on the unit sphere   where a convex body  with   boundary provides a solution if   for the support function   of    The logarithmic Minkowski problem  was posed by Firey in his 1974 seminal paper.  It seeks to characterize the cone volume measure   of a convex body  containing the origin o. The logarithmic Minkowski problem   is a challenging problem in convex geometry and receives much attention since 2012.

   In this talk, we will present our very recent work on the logarithmic Minkowski problem. We prove the existence of solutions to the logarithmic Minkowski problem for quadrilaterals, and characterize the numbers of solutions completely. 

This talk is based on the joint work with Liu Yude, Lu Xinbao and Sun Qiang.

 

熊革，同济大学数学学院教授，博士生导师，是凸几何领域的知名专家，他解决了若干重要问题，获得若干重要结果，论文发表于Bull. LMS, JDG, Adv. Math., CVPDE等权威杂志。