Lindelöf's theorem for catenoids revisited

Abstract

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.

References in corpus (3)

• Lindelöf's theorem for catenoids revisited
• Minimal hypersurfaces in $\HH^n \times \R$, total curvature and index
• Stable minimal hypersurfaces in the hyperbolic space

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• Counting Minimal Surfaces in Quasi-Fuchsian three-Manifolds
• Stability of Catenoids and Helicoids in Hyperbolic Space
• Stability of the classical catenoid and Darboux-Pöschl-Teller potentials
• Asymptotic Plateau Problem for Two Contours