THE MINIMAL VOLUME ORIENTABLE HYPERBOLIC 3-MANIFOLD WITH 4 CUSPS

被引：9
作者：
Yoshida, Ken'ichi [1 ]
机构：
[1] Univ Tokyo, Grad Sch Math Sci, Tokyo 1538914, Japan
来源：
PACIFIC JOURNAL OF MATHEMATICS | 2013年 / 266卷 / 02期
关键词：
hyperbolic; 3-manifold; essential surface; geodesic boundary; MANIFOLDS; SURFACES;
D O I：
10.2140/pjm.2013.266.457
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that the 8(2)(4) link complement is the minimal volume orientable hyperbolic manifold with 4 cusps. Its volume is twice the volume V-8 of the ideal regular octahedron; that is, 7.32 ... = 2V(8). The proof relies on Agol's argument used to determine the minimal volume hyperbolic 3-manifolds with 2 cusps. We also need to estimate the volume of a hyperbolic 3-manifold with totally geodesic boundary which contains an essential surface with non-separating boundary.
引用
收藏
页码：457 / 476
页数：20
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