Lindelöf’s theorem for hyperbolic catenoids

Bérard, Pierre; Sa Earp, Ricardo

doi:10.1090/S0002-9939-2010-10492-6

Lindelöf’s theorem for hyperbolic catenoids
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by Pierre Bérard and Ricardo Sa Earp

Proc. Amer. Math. Soc. 138 (2010), 3657-3669

DOI: https://doi.org/10.1090/S0002-9939-2010-10492-6

Published electronically: June 15, 2010

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Abstract:

In this paper, we study the maximal stable domains on minimal and constant mean curvature $1$ catenoids in hyperbolic space. In particular we investigate whether half-vertical catenoids are maximal stable domains (Lindelöf’s property). Our motivation comes from Lindelöf’s 1870 paper on catenoids in Euclidean space.

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