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2003 Foliations of Hyperbolic Space by Constant Mean Curvature Surfaces Sharing Ideal Boundary
David Chopp, John A. Velling
Experiment. Math. 12(3): 339-350 (2003).

Abstract

Let {\small $\gamma$} be a Jordan curve in {\small $\sph{2}$}, considered as the ideal boundary of {\small $\hyp{3}$}. Under certain circumstances, it is known that for any {\small $c \in (-1,1)$}, there is a disc of constant mean curvature c embedded in {\small $\hyp{3}$} with {\small $\gamma$} as its ideal boundary. Using analysis and numerical experiments, we examine whether or not these surfaces in fact foliate {\small $\hyp{3}$}, and to what extent the known conditions on the curve can be relaxed.

Citation

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David Chopp. John A. Velling. "Foliations of Hyperbolic Space by Constant Mean Curvature Surfaces Sharing Ideal Boundary." Experiment. Math. 12 (3) 339 - 350, 2003.

Information

Published: 2003
First available in Project Euclid: 15 June 2004

MathSciNet: MR2034397
zbMATH: 1081.53029

Subjects:
Primary: 53C12, 53C44

Rights: Copyright © 2003 A K Peters, Ltd.

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Vol.12 • No. 3 • 2003
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