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Existence of infinitely many minimal hypersurfaces in positive Ricci curvature

Author(s): Coda Marques, Fernando; Neves, André

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dc.contributor.authorCoda Marques, Fernando-
dc.contributor.authorNeves, André-
dc.identifier.citationMarques, Fernando C, Neves, Andre. (2017). Existence of infinitely many minimal hypersurfaces in positive Ricci curvature. INVENTIONES MATHEMATICAE, 209 (577 - 616. doi:10.1007/s00222-017-0716-6en_US
dc.description.abstractIn the early 1980s, S. T. Yau conjectured that any compact Riemannian three-manifold admits an infinite number of closed immersed minimal surfaces. We use min-max theory for the area functional to prove this conjecture in the positive Ricci curvature setting. More precisely, we show that every compact Riemannian manifold with positive Ricci curvature and dimension at most seven contains infinitely many smooth, closed, embedded minimal hypersurfaces. In the last section we mention some open problems related with the geometry of these minimal hypersurfaces.en_US
dc.format.extent577 - 616en_US
dc.rightsAuthor's manuscripten_US
dc.titleExistence of infinitely many minimal hypersurfaces in positive Ricci curvatureen_US
dc.typeJournal Articleen_US

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