Lindelöf's theorem for catenoids revisited

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 catenoids in Euclidean and hyperbolic spaces and in $H^2 \times R$. We in particular investigate whether half-vertical catenoids are maximal stable domains (\emph{Lindelöf's property}). We also consider stable domains on catenoid-cousins in hyperbolic space. Our motivations come from Lindelöf's 1870 paper on catenoids in Euclidean space.

Mots clés: Index.

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

Domaines: Géométrie différentielle [math.DG]

Pierre Bérard, Ricardo Sa Earp. Lindelöf's theorem for catenoids revisited. 2009. ⟨hal-00407395⟩