Hyperbolic Plateau problems
微分几何
2011-05-24 v2 辛几何
摘要
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.
引用
@article{arxiv.math/0506231,
title = {Hyperbolic Plateau problems},
author = {Graham Smith},
journal= {arXiv preprint arXiv:math/0506231},
year = {2011}
}
备注
Complete redraft of the preceding version. Much shorter. Ideas essentially identical though slightly refined. Hopefully clearer