A ramification theorem for the ratio of canonical forms of flat surfaces in hyperbolic three-space
Differential Geometry
2013-08-12 v3 Complex Variables
Abstract
We provide an effective ramification theorem for the ratio of canonical forms of a weakly complete flat front in the hyperbolic three-space. Moreover we give the two applications of this theorem, the first one is to show an analogue of the Ahlfors islands theorem for it and the second one is to give a simple proof of the classification of complete nonsingular flat surfaces in the hyperbolic three-space.
Keywords
Cite
@article{arxiv.1110.3110,
title = {A ramification theorem for the ratio of canonical forms of flat surfaces in hyperbolic three-space},
author = {Yu Kawakami},
journal= {arXiv preprint arXiv:1110.3110},
year = {2013}
}
Comments
11 pages, no figure, to appear in Geometriae Dedicata. arXiv admin note: substantial text overlap with arXiv:1004.1484