The Morse indices for free boundary minimal surfaces

题目:The Morse indices for free boundary minimal surfaces

报告人:周德堂 教授,Universidade Federal Fluminense

时间:2018年7月19日14:00-15:00

地点:知新楼B座1032

邀请人:张晓燕教授

Abstract:The study of free boundary minimal submanifolds has been a very active topic in the recent years. Since they are critical points area functional, Morse index plays an important role in classifications. I will discuss our recent progress in determining the Morse index for critical catenoids and some related questions. For example, I present a joint work with Graham Smith, Ari Stern, and Hung Tran that the Morse index $MI(n)$ of an $n$-dimensional critical cateniod satisfies: $MI(2)=4$, $MI(3)=5$, $MI(4)=6$, $MI(5)=21$, …, and $MI(100)=350,319,724,626 $. In general, we obtain a asymptotic formula for $MI(n)$.