Next Article in Journal
Topics of Measure Theory on Infinite Dimensional Spaces
Next Article in Special Issue
Multiplicative Structure and Hecke Rings of Generator Matrices for Codes over Quotient Rings of Euclidean Domains
Previous Article in Journal
On the Uniqueness Results and Value Distribution of Meromorphic Mappings
Previous Article in Special Issue
Lattices and Rational Points
Article Menu
Issue 3 (September) cover image

Export Article

Open AccessArticle
Mathematics 2017, 5(3), 43; doi:10.3390/math5030043

On Minimal Covolume Hyperbolic Lattices

Department of Mathematics, University of Fribourg, CH-1700 Fribourg, Switzerland
Received: 10 July 2017 / Revised: 14 August 2017 / Accepted: 15 August 2017 / Published: 22 August 2017
(This article belongs to the Special Issue Geometry of Numbers)
View Full-Text   |   Download PDF [457 KB, uploaded 24 August 2017]   |  


We study lattices with a non-compact fundamental domain of small volume in hyperbolic space H n . First, we identify the arithmetic lattices in Isom + H n of minimal covolume for even n up to 18. Then, we discuss the related problem in higher odd dimensions and provide solutions for n = 11 and n = 13 in terms of the rotation subgroup of certain Coxeter pyramid groups found by Tumarkin. The results depend on the work of Belolipetsky and Emery, as well as on the Euler characteristic computation for hyperbolic Coxeter polyhedra with few facets by means of the program CoxIter developed by Guglielmetti. This work complements the survey about hyperbolic orbifolds of minimal volume. View Full-Text
Keywords: hyperbolic lattice; cusp; minimal volume; arithmetic group; Coxeter polyhedron hyperbolic lattice; cusp; minimal volume; arithmetic group; Coxeter polyhedron

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Kellerhals, R. On Minimal Covolume Hyperbolic Lattices. Mathematics 2017, 5, 43.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top