#### DOCUMENTA MATHEMATICA, Vol. 19 (2014), 801-814

Mikhail Belolipetsky, Vincent Emery

Hyperbolic Manifolds of Small Volume

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\$.

2010 Mathematics Subject Classification: 22E40 (primary); 11E57, 20G30, 51M25 (secondary)

Keywords and Phrases: hyperbolic manifold, volume, Euler characteristic, arithmetic group.

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