Rigidity of min-max minimal spheres in three-manifolds

Fernando C. Marques; Ndré Neves

doi:10.1215/00127094-1813410

Rigidity of min-max minimal spheres in three-manifolds

Fernando C. Marques, Ndré Neves

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71 Scopus citations

Abstract

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 4π and index at most one. If the Ricci curvature is positive we also prove sharp estimates for the width.

Original language	English (US)
Pages (from-to)	2725-2752
Number of pages	28
Journal	Duke Mathematical Journal
Volume	161
Issue number	14
DOIs	https://doi.org/10.1215/00127094-1813410
State	Published - Nov 1 2012
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1215/00127094-1813410

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title = "Rigidity of min-max minimal spheres in three-manifolds",

abstract = "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 4π and index at most one. If the Ricci curvature is positive we also prove sharp estimates for the width.",

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Rigidity of min-max minimal spheres in three-manifolds

Abstract

All Science Journal Classification (ASJC) codes

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