Minimal hypersurfaces with bounded index

被引：32
作者：
Chodosh, Otis [1 ,2 ]
Ketover, Daniel [2 ]
Maximo, Davi [3 ,4 ]
机构：
[1] Univ Cambridge, Dept Pure Math & Math Stat, Cambridge, England
[2] Princeton Univ, Dept Math, Princeton, NJ 08544 USA
[3] Stanford Univ, Dept Math, Stanford, CA 94305 USA
[4] Univ Penn, Dept Math, Philadelphia, PA 19104 USA
来源：
INVENTIONES MATHEMATICAE | 2017年 / 209卷 / 03期
基金：
英国工程与自然科学研究理事会; 美国国家科学基金会;
关键词：
MORSE INDEX; SURFACES; CURVATURE; EXISTENCE; REGULARITY; AREA; 3-MANIFOLDS; LAMINATIONS; COMPACTNESS; UNIQUENESS;
D O I：
10.1007/s00222-017-0717-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove a structural theorem that provides a precise local picture of how a sequence of closed embedded minimal hypersurfaces with uniformly bounded index (and volume if the ambient dimension is greater than three) in a Riemannian manifold (M-n, g), 3 <= n <= 7 can degenerate. Loosely speaking, our results show that embedded minimal hypersurfaces with bounded index behave qualitatively like embedded stable minimal hypersurfaces, up to controlled errors. Several compactness/finiteness theorems follow from our local picture.
引用
收藏
页码：617 / 664
页数：48
相关论文
共 58 条
[1]   FIRST VARIATION OF A VARIFOLD [J].
ALLARD, WK .
ANNALS OF MATHEMATICS, 1972, 95 (03) :417-&
[2]  
[Anonymous], INVENT MATH
[3]  
Bogopolski O, 2008, EMS TEXTB MATH, P1
[4]   NON-ORIENTABLE SURFACES IN ORIENTABLE 3-MANIFOLDS [J].
BREDON, GE ;
WOOD, JW .
INVENTIONES MATHEMATICAE, 1969, 7 (02) :83-&
[5]  
Buzano R., 2015, ARXIV151201047
[6]  
Carlotto A., 2015, ANN SCUOLA NORM SUP
[7]   Effective versions of the positive mass theorem [J].
Carlotto, Alessandro ;
Chodosh, Otis ;
Eichmair, Michael .
INVENTIONES MATHEMATICAE, 2016, 206 (03) :975-1016
[8]  
Chodosh O, 2016, J DIFFER GEOM, V104, P399
[9]  
CHOI HI, 1983, J DIFFER GEOM, V18, P559
[10]   THE SPACE OF MINIMAL EMBEDDINGS OF A SURFACE INTO A 3-DIMENSIONAL MANIFOLD OF POSITIVE RICCI CURVATURE [J].
CHOI, HI ;
SCHOEN, R .
INVENTIONES MATHEMATICAE, 1985, 81 (03) :387-394
123456