Hyperbolic Plateau problems

Details Hyperbolic Plateau problems Hyperbolic Plateau problems

2005-06-13

arxiv.org/abs/math/0506231v2

Mathematics

Differential Geometry

Complete redraft of the preceding version. Much shorter. Ideas essentially identical though slightly refined. Hopefully cleare

Scientific paper

We consider surfaces of constant Gaussian curvature immersed in 3-dimensional manifolds, and we strengthen the compactness result of Labourie in the case where the ambient manifold is 3-dimensional hyperbolic space. This allows us to prove results of existence of solutions to the asymptotic Plateau problem, as defined by Labourie, and the continuous dependence of these solutions on the data.

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