Lindelöf's theorem for hyperbolic catenoids

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

1 IF - Institut Fourier
2 Departamento de Matematica

In this paper we study the maximal stable domains on minimal and constant mean curvature $1$ catenoids in hyperbolic space. We in particular investigate whether half-vertical catenoids are maximal stable domains. Our motivations come from Lindelöf's 1870 paper on catenoids in Euclidean space.

Mots clés: Index; Minimal surfaces; Constant mean curvature surfaces; Stability; Index.

Domaines: Géométrie différentielle [math.DG]

Pierre Bérard, Ricardo Sa Earp. Lindelöf's theorem for hyperbolic catenoids. Proceedings of the American Mathematical Society, 2010, 138, pp.3657-3669. ⟨10.1090/S0002-9939-2010-10492-6⟩. ⟨hal-00429404⟩