Foliations of Hyperbolic Space by Constant Mean Curvature Surfaces Sharing Ideal Boundary

Chopp, David; Velling, John A.

Experiment. Math., Tome 12 (2003) no. 1, p. 339-350 / Harvested from Project Euclid

Résumé

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.

Publié le : 2003-05-14
Classification: Foliations, constant mean curvature, hyperbolic space, level set method, 53C12, 53C44

@article{1087329236,
     author = {Chopp, David and Velling, John A.},
     title = {Foliations of Hyperbolic Space by Constant Mean Curvature Surfaces Sharing Ideal Boundary},
     journal = {Experiment. Math.},
     volume = {12},
     number = {1},
     year = {2003},
     pages = { 339-350},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1087329236}
}

Chopp, David; Velling, John A. Foliations of Hyperbolic Space by Constant Mean Curvature Surfaces Sharing Ideal Boundary. Experiment. Math., Tome 12 (2003) no. 1, pp.  339-350. http://gdmltest.u-ga.fr/item/1087329236/