POSTECH Math

Infomation

Category 날짜 시간 2017 Math Colloquium 2017-03-03 15:50:00 ~ 18:00:00 Math Sci Bldg 404 Jai gyoung Choe Host Kang Tae Kim KIAS I:극소곡면이야기, II: A dichotomy in manifolds of nonnegative Ricci curvature

Abstract

I Title: 극소곡면 이야기
I Abstract: 극소곡면은 넓이를 최소로 갖는 곡면이다. 이 곡면의 여러가지 재미있는 성질을 소개할 것이다.

II Title: A dichotomy in manifolds of nonnegative Ricci curvature
II Abstract: I will first review some old theorems on manifolds of nonnegative Ricci curvature: Theorems by Hadamard, Myers, O'Neill, Cheeger-Gromoll, Frankel, Lawson, Petersen-Wilhelm.
Then I'll prove a new theorem: Let $M$ be a compact Riemannian manifold of nonnegative Ricci curvature and $\Sigma$ a compact embedded 2-sided minimal hypersurface in $M$. It is proved that there is a dichotomy: If $\Sigma$ does not separate $M$ then $\Sigma$ is totally geodesic and $M\setminus\Sigma$ is isometric to the Riemannian product $\Sigma\times(a,b)$, and if $\Sigma$ separates $M$ then the map $i_*:\pi_1(\Sigma)\rightarrow \pi_1(M)$ induced by inclusion is surjective. (Joint with A. Fraser)