Existence of infinitely many minimal hypersurfaces in positive Ricci curvature

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Title: Existence of infinitely many minimal hypersurfaces in positive Ricci curvature
Authors: Marques, FC
Neves, A
Item Type: Journal Article
Abstract: In 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.
Issue Date: 25-Jan-2017
Date of Acceptance: 31-Dec-2016
ISSN: 0020-9910
Publisher: Springer Verlag
Start Page: 577
End Page: 616
Journal / Book Title: Inventiones Mathematicae
Volume: 209
Issue: 2
Copyright Statement: The final publication is available at Springer via
Sponsor/Funder: Commission of the European Communities
Engineering & Physical Science Research Council (E
The Leverhulme Trust
Funder's Grant Number: FP7-ERC-2011-STG-278940
MAAA_3187 EP/K00865X/1
Keywords: Science & Technology
Physical Sciences
0101 Pure Mathematics
General Mathematics
Publication Status: Published
Appears in Collections:Pure Mathematics

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