Rigidity of min-max minimal spheres in three-manifolds

Fernando C. Marques, Ndré Neves

Research output: Contribution to journalArticle

29 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 languageEnglish (US)
Pages (from-to)2725-2752
Number of pages28
JournalDuke Mathematical Journal
Volume161
Issue number14
DOIs
StatePublished - Nov 1 2012

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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