偏微分方程研讨班：On a width lemma and its application

中科院数学与系统科学研究院

数学研究所

学术报告

偏微分方程研讨班

报告人：李志夙 副教授（西北大学）

题  目：On a width lemma and its application

时  间：2023.08.08（星期二）16:00-17:00

地  点：数学院南楼N913

摘  要：There's a profound theorem in convex geometry of Caratheodory states that the convex hull of a set $A$ in $R^n$ is the union of all simplices with vertices in $A$. An interesting question related to this fact is whether there is such a simplex of width larger than the width of $A$ multiplied by some universal small positive constants? In this talk, we will show that for any set in $R^n$ of width $1$,  one can also extract from it $n+1$ points of width greater than a universal positive constant $1/C$,  i.e., the so called width lemma, which gives a positive answer to the above question, and an application in analysis and PDE.