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June 2017 Minimal hypersurfaces of least area
Laurent Mazet, Harold Rosenberg
J. Differential Geom. 106(2): 283-316 (June 2017). DOI: 10.4310/jdg/1497405627

Abstract

In this paper, we study closed embedded minimal hypersurfaces in a Riemannian $(n+1)$-manifold $(2 \leq n \leq 6)$ that minimize area among such hypersurfaces. We show they exist and arise either by minimization techniques or by min–max methods: they have index at most $1$. We apply this to obtain a lower area bound for such minimal surfaces in some hyperbolic $3$-manifolds.

Funding Statement

The authors were partially supported by the ANR-11-IS01-0002 grant.

Citation

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Laurent Mazet. Harold Rosenberg. "Minimal hypersurfaces of least area." J. Differential Geom. 106 (2) 283 - 316, June 2017. https://doi.org/10.4310/jdg/1497405627

Information

Received: 27 April 2015; Published: June 2017
First available in Project Euclid: 14 June 2017

zbMATH: 06846952
MathSciNet: MR3662993
Digital Object Identifier: 10.4310/jdg/1497405627

Rights: Copyright © 2017 Lehigh University

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Vol.106 • No. 2 • June 2017
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