科学研究
报告题目:

Quantitative geometric inequalities in $\mathbb R^n$: Power growth other than 2

报告人:

张翼 副研究员(中国科公司数学所)

报告时间:

报告地点:

公司雷军科技楼446报告厅

报告摘要:

In the field of geometric inequality stability, it is common to observe a lower bound for the energy difference that grows with a power of 2. For instance, a notable finding by Fusco, Maggi, and Pratelli says that, for any set of finite perimeter $E \subset \mathbb{R}^n$ with $|E| = |B|$ and a barycenter at the origin, one has $P(E) - P(B) \ge c(n)|E\Delta B|^2$. This phenomenon also appears in some other follow-up work. This pattern is also evident in subsequent research. In my presentation, I will discuss recent findings concerning scenarios in Euclidean spaces where the power is no longer $2$ in Euclidean spaces.