Hyperbolic manifolds of small volume
Metric Geometry
2015-04-09 v1 Geometric Topology
Abstract
We conjecture that for every dimension n not equal 3 there exists a noncompact hyperbolic n-manifold whose volume is smaller than the volume of any compact hyperbolic n-manifold. For dimensions n at most 4 and n=6 this conjecture follows from the known results. In this paper we show that the conjecture is true for arithmetic hyperbolic n-manifolds of dimension n at least 30.
Cite
@article{arxiv.1310.2270,
title = {Hyperbolic manifolds of small volume},
author = {Mikhail Belolipetsky and Vincent Emery},
journal= {arXiv preprint arXiv:1310.2270},
year = {2015}
}
Comments
14 pages