Minimal hypersurfaces of least area

Laurent Mazet (1) , Harold Rosenberg (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 IMPA Jean-Christophe Yoccoz

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.

Domaines: Géométrie différentielle [math.DG]

Laurent Mazet, Harold Rosenberg. Minimal hypersurfaces of least area. Journal of Differential Geometry, 2017, 106 (2), pp.283-315. ⟨10.4310/jdg/1497405627⟩. ⟨hal-01130024⟩