## Infomation

Category | 2017 Math Colloquium | ||
---|---|---|---|

날짜 | 2017-03-03 | 시간 | 15:50:00 ~ 18:00:00 |

장소 | Math Sci Bldg 404 | ||

Speaker | Jai gyoung Choe | Host | Kang Tae Kim |

소속 | KIAS | ||

TOPIC | 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 non-negative 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 Σ a compact embedded 2-sided minimal hypersurface in M. It is proved that there is a di-chotomy: If Σ does not separate M then Σ is totally geodesic and M \ Σ is isometric to the Riemannian product Σ × (a, b), and if Σ separates M then the map i∗ : π1(Σ) → π1(M) induced by inclusion is surjective. (Joint with A. Fraser)

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 non-negative 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 Σ a compact embedded 2-sided minimal hypersurface in M. It is proved that there is a di-chotomy: If Σ does not separate M then Σ is totally geodesic and M \ Σ is isometric to the Riemannian product Σ × (a, b), and if Σ separates M then the map i∗ : π1(Σ) → π1(M) induced by inclusion is surjective. (Joint with A. Fraser)