1 November 2012 Rigidity of min-max minimal spheres in three-manifolds
Fernando C. Marques, André Neves
Duke Math. J. 161(14): 2725-2752 (1 November 2012). DOI: 10.1215/00127094-1813410


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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Fernando C. Marques. André Neves. "Rigidity of min-max minimal spheres in three-manifolds." Duke Math. J. 161 (14) 2725 - 2752, 1 November 2012. https://doi.org/10.1215/00127094-1813410


Published: 1 November 2012
First available in Project Euclid: 26 October 2012

zbMATH: 1260.53079
MathSciNet: MR2993139
Digital Object Identifier: 10.1215/00127094-1813410

Primary: 53C24 , 53C42
Secondary: 35J15 , 35J20

Rights: Copyright © 2012 Duke University Press

Vol.161 • No. 14 • 1 November 2012
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