RIGIDITY OF MIN-MAX MINIMAL SPHERES IN THREE-MANIFOLDS

被引：58
|
作者：
Marques, Fernando C. [1 ]
Neves, Andre [2 ]
机构：
[1] Inst Matematica Pura & Aplicada, BR-22460320 Rio De Janeiro, Brazil
[2] Univ London Imperial Coll Sci Technol & Med, Dept Pure Math, London SW7 2AZ, England
来源：
DUKE MATHEMATICAL JOURNAL | 2012年 / 161卷 / 14期
关键词：
SCALAR CURVATURE RIGIDITY; SURFACES; MASS; MANIFOLDS; EXISTENCE; PROOF; SPACE; TORI;
D O I：
10.1215/00127094-1813410
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we consider min-max minimal surfaces in three-manifolds and prove some rigidity results. For instance, we prove that any metric on a three-sphere which has scalar curvature greater than or equal to 6 and is not round must have an embedded minimal sphere of area strictly smaller than 4 pi and index at most one. If the Ricci curvature is positive we also prove sharp estimates for the width.
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页码：2725 / 2752
页数：28
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