Geodesic
Hyperbolic manifolds of small volume
Documenta mathematica, Tome 19 (2014), pp. 801-814.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We conjecture that for every dimension $n \neq 3$ there exists a noncompact hyperbolic $n$-manifold whose volume is smaller than the volume of any compact hyperbolic $n$-manifold. For dimensions $n \le 4$ 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 $n\ge 30$.
Classification : 22E40, 11E57, 20G30, 51M25
Keywords: hyperbolic manifold, volume, Euler characteristic, arithmetic group 
@article{DOCMA_2014__19__a19,
     author = {Belolipetsky, Mikhail and Emery, Vincent},
     title = {Hyperbolic manifolds of small volume},
     journal = {Documenta mathematica},
     pages = {801--814},
     publisher = {mathdoc},
     volume = {19},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a19/}
}
TY  - JOUR
AU  - Belolipetsky, Mikhail
AU  - Emery, Vincent
TI  - Hyperbolic manifolds of small volume
JO  - Documenta mathematica
PY  - 2014
SP  - 801
EP  - 814
VL  - 19
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a19/
LA  - en
ID  - DOCMA_2014__19__a19
ER  - 
%0 Journal Article
%A Belolipetsky, Mikhail
%A Emery, Vincent
%T Hyperbolic manifolds of small volume
%J Documenta mathematica
%D 2014
%P 801-814
%V 19
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a19/
%G en
%F DOCMA_2014__19__a19
Belolipetsky, Mikhail; Emery, Vincent. Hyperbolic manifolds of small volume. Documenta mathematica, Tome 19 (2014), pp. 801-814. http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a19/