Rigidity of min-max minimal spheres in three-manifolds

Fernando C. Marques, Ndré Neves

Research output: Contribution to journalArticlepeer-review

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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
Issue number14
StatePublished - Nov 1 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics


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