English

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.

Keywords

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

R2 v1 2026-06-22T01:42:52.638Z