报告题目：The logarithmic Minkowski problem in R^2

报告人：熊革（同济大学）

报告时间：2023年4月20日14:30-15:30

报告地点：立德楼702教室

报告摘要：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.

报告人简介：熊革，同济大学长聘教授，博士生导师。主要研究凸体几何。熊革教授解决了凸体几何中的几个公开问题，包括Lutwak-Yang-Zhang关于锥体积泛函极值问题的2, 3维情形；由截面确定凸体的Baker-Larman问题的2维情形；他与学生最早提出、并解决了Lp静电容量的Minkowski 问题；完全解决了纽约大学G. Zhang教授关于凸体的John 椭球与对偶惯性椭球一致性的问题。

熊革教授在国际纯数学的重要期刊JDG, AIM, IUMJ, IMRN, CVPDE, JFA，CAG, Israel Journal of Mathematics, Discrete and Computational Geometry等上发表论文30余篇。部分成果被写入凸体几何的经典教材《Geometric Tomography》和《Convex Bodies: the Brunn-Minkowski theory》中。