Minimal hypersurfaces in $\HH^n \times \R$, total curvature and index

Pierre Bérard (1) , Ricardo Sa Earp (2)

1 IF - Institut Fourier
2 Departamento de Matematica

In this paper, we consider minimal hypersurfaces in the product space $\mathbb{H}^n \times \mathbb{R}$. We study the relation between the notions of finite total curvature and index of the stability operator. We study examples of rotation hypersurfaces and hypersurfaces invariant under hyperbolic translations; they serve as counter-examples and are useful barriers for many geometric problems.

Mots clés: Minimal hypersurfaces; stability; index

Domaines: Géométrie différentielle [math.DG]

Pierre Bérard, Ricardo Sa Earp. Minimal hypersurfaces in $\HH^n \times \R$, total curvature and index. 2008. ⟨hal-00315294v1⟩