Completeness of convex entire surfaces in Minkowski 3-space
Differential Geometry
2022-07-21 v1 Geometric Topology
Abstract
We prove four results towards a description, in terms of the null support function, of the set of isometric embeddings of the hyperbolic plane into Minkowski 3-space. We show that for sufficiently tame null support function, the corresponding entire surface of constant curvature -1 is complete, and for sufficiently sharp null support function, it is incomplete. Our results apply also to entire surfaces whose curvature is merely bounded.
Keywords
Cite
@article{arxiv.2207.10019,
title = {Completeness of convex entire surfaces in Minkowski 3-space},
author = {Francesco Bonsante and Andrea Seppi and Peter Smillie},
journal= {arXiv preprint arXiv:2207.10019},
year = {2022}
}
Comments
53 pages, 9 figures