Minimal hypersurfaces of least area

2015/03/10 by Mazet, Laurent, Rosenberg, Harold · 2 citations
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1503.02938

Abstract

In this paper, we study closed embedded minimal hypersurfaces in a Riemannian (n+1)-manifold (2≤ n≤ 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.

Cited by

• Regularity of Cohomogeneity two equivariant isotopy minimization problems and minimal hypersurfaces with large first Betti number on spheres
• Volume spectrum of fiber bundles and the widths of Berger spheres

Related

• Embeddedness of least area minimal hypersurfaces
• Min-max minimal hypersurface in (Mⁿ⁺¹, g) with Ric_g>0 and 2≤ n≤ 6
• Localization of min-max minimal hypersurfaces
• Non-compactness of the space of minimal hypersurfaces
• Min-max minimal hypersurfaces in non-compact manifolds