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
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