Journal of Differential Geometry

Minimal hypersurfaces of least area

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.

Note

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

Article information

Source
J. Differential Geom., Volume 106, Number 2 (2017), 283-316.

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

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1497405627

Digital Object Identifier
doi:10.4310/jdg/1497405627

Mathematical Reviews number (MathSciNet)
MR3662993

Zentralblatt MATH identifier
06846952

Citation

Mazet, Laurent; Rosenberg, Harold. Minimal hypersurfaces of least area. J. Differential Geom. 106 (2017), no. 2, 283--316. doi:10.4310/jdg/1497405627. https://projecteuclid.org/euclid.jdg/1497405627