컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0508 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | Geometry (SS-06) |
| 영문제목 (Title(Eng.)) |
Isoperimetric inequalities for complete proper minimal submanifolds in hyperbolic space |
| 저자(Author(s)) |
Sung-Hong Min1, Keomkyo Seo2 Korea Institute for Advanced Study1, Sookmyung Women's University2 |
| 초록본문(Abstract) | Let $\Sigma$ be a $k$-dimensional complete proper minimal submanifold in the Poincar\'{e} ball model $B^n$ of hyperbolic geometry. If we consider $\Sigma$ as a subset of the unit ball $B^n$ in Euclidean space, one can measure the Euclidean volumes of the given minimal submanifold $\Sigma$ and the ideal boundary $\partial_\infty \Sigma$. Using this concept, we prove an optimal linear isoperimetric inequality which gives the classical isoperimetric inequality under geometric assumption. By proving the monotonicity theorem for such $\Sigma$, we further obtain a sharp lower bound for the Euclidean volume, which is an extension of Fraser-Schoen and Brendle's recent results to hyperbolic space. Moreover we introduce the M\"{o}bius volume of $\Sigma$ in $B^n$ to prove an isoperimetric inequality via the M\"{o}bius volume for $\Sigma$. Most parts of this talk is based on the paper "Optimal isoperimetric inequalities for complete proper minimal submanifolds in hyperbolic space (arXiv:1201.2732)" which is a joint work with Sung-Hong Min. |
| 분류기호 (MSC number(s)) |
58E35, 49Q05, 53C42 |
| 키워드(Keyword(s)) | isoperimetric inequality, minimal submanifold, hyperbolic space, monotonicity |
| 강연 형태 (Language of Session (Talk)) |
English |