The Cauchy problem for Liouville equation and Bryant surfaces
Differential Geometry
2007-05-23 v1 Analysis of PDEs
Abstract
We give a construction that connects the Cauchy problem for Liouville elliptic equation with a certain initial value problem for mean curvature one surfaces in hyperbolic 3-space H3, and solve both of them. We construct the only mean curvature one surface in H3 that passes through a given curve with given unit normal along it, and provide diverse applications. In particular, topics like period problems, symmetries, finite total curvature, planar geodesics, rigidity, etc. of surfaces are treated.
Cite
@article{arxiv.math/0310092,
title = {The Cauchy problem for Liouville equation and Bryant surfaces},
author = {Jose A. Galvez and Pablo Mira},
journal= {arXiv preprint arXiv:math/0310092},
year = {2007}
}
Comments
34 pages, 4 figures