Counting hyperbolic manifolds with bounded diameter
| dc.creator | Young, Robert | |
| dc.date | 2006-01-23 | |
| dc.date.accessioned | 2026-07-07T06:59:12Z | |
| dc.date.available | 2026-07-07T06:59:12Z | |
| dc.description | Let $ρ_n(V)$ be the number of complete hyperbolic manifolds of dimension n with volume less than $V$. Burger, Gelander, Lubotzky, and Moses showed that when n>3 there exist a,b>0 depending on the dimension such that aV log(V) < log(ρ_n(V)) < bV log(V), for V >> 0. In this note, we use their methods to bound the number of hyperbolic manifolds with diameter less than d and show that the number grows double-exponentially. Additionally, this bound holds in dimension 3. | |
| dc.description | 4 pages | |
| dc.identifier | https://arxiv.org/abs/math/0601560 | |
| dc.identifier | http://arxiv.org/abs/math/0601560 | |
| dc.identifier | Geometriae Dedicata, 116(2005), 61 - 65 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/107662 | |
| dc.subject | Differential Geometry | |
| dc.subject | 57N16 (Primary) 22E40 (Secondary) | |
| dc.title | Counting hyperbolic manifolds with bounded diameter | |
| dc.type | text |