The orientable cusped hyperbolic 3-manifolds of minimum volume

By Chunling Cao, G. Meyerhoff. 2001

121 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3b6bfe13782c84115abde65da70ee9151e413a53

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The maximal number of exceptional Dehn surgeries (2008, methodology): “Here, one seeks not to establish that the filled-in manifold M(s) has a hyperbolic structure, but rather that it is ‘hyperbolike’.”
Universal bounds for hyperbolic Dehn surgery (2002, methodology): “Recently, Cao-Meyerhoff [11] showed that the orientable cusped hyperbolic 3-manifolds of smallest volume are the the figure eight knot complement and another closely related manifold, with volume vω = 2.02988 . . . .”
The minimal volume orientable hyperbolic 2-cusped 3-manifolds (2008, background): “The smallest volume one-cusped orientable hyperbolic manifolds were identified by Cao and Meyerhoff [5], one of which is the figure-eight knot complement, with volume 2.0298 . . . = 2V3, where V3 = 1.01494 . . . is the volume of a regular ideal tetrahedron.”
Three-Dimensional Orbifolds and Their Geometric Structures (2003, background): “Meyerhoff [40] proved that the figure eight knot exterior and its sister are the orientable cusped manifolds of least volume.”
Minimum volume cusped hyperbolic three-manifolds (2007, methodology): “The following lemma appears in [ CM ]; a related lemma for compact manifolds appears in [GMM].”
An Introduction to Geometric Topology (2016, methodology): “This has been proved for c = 1 by Cao and Meyerhoff [11], for c = 2 by Agol [1], and for c = 4 by Yoshida [60].”
3-Manifold Groups (2012, background): “heorem 0.2]. (4) NotethatitfollowsfromGabai–Meyerhoﬀ–Milley [GMM09, Corollary1.3] [Mie09, Theorem 1.3] that for a non-graph manifold Nwe have vol(N) > 0.942. (See also [Ada87, Theorem 3], [Ada88], [CaM01], [GMM10] and [Ag10b, Theorem 3.6] for more information and more results.) Note that an aﬃrma”