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==introduction== | ==introduction== | ||
| − | * smallest volume of a closed, complex hyperbolic 2-manifold is | + | * smallest volume of a closed, complex hyperbolic 2-manifold is <math>8\pi^2</math> |
| − | * the smallest volume of a cusped (and so of any) complex hyperbolic 2-manifold is | + | * the smallest volume of a cusped (and so of any) complex hyperbolic 2-manifold is <math>8\pi^2/3</math> |
==minimal volume cupsed orbifolds== | ==minimal volume cupsed orbifolds== | ||
| − | * there are two cusped, complex hyperbolic orbifolds with volume | + | * there are two cusped, complex hyperbolic orbifolds with volume <math>\pi^2/27</math> |
* Eisenstein-Picard lattice | * Eisenstein-Picard lattice | ||
* Falbel, Elisha, and John R. Parker. 2006. “The Geometry of the Eisenstein-Picard Modular Group.” Duke Mathematical Journal 131 (2): 249–289. doi:10.1215/S0012-7094-06-13123-X. | * Falbel, Elisha, and John R. Parker. 2006. “The Geometry of the Eisenstein-Picard Modular Group.” Duke Mathematical Journal 131 (2): 249–289. doi:10.1215/S0012-7094-06-13123-X. | ||
2020년 11월 14일 (토) 01:12 기준 최신판
introduction
- smallest volume of a closed, complex hyperbolic 2-manifold is \(8\pi^2\)
- the smallest volume of a cusped (and so of any) complex hyperbolic 2-manifold is \(8\pi^2/3\)
minimal volume cupsed orbifolds
- there are two cusped, complex hyperbolic orbifolds with volume \(\pi^2/27\)
- Eisenstein-Picard lattice
- Falbel, Elisha, and John R. Parker. 2006. “The Geometry of the Eisenstein-Picard Modular Group.” Duke Mathematical Journal 131 (2): 249–289. doi:10.1215/S0012-7094-06-13123-X.
- Zhao, Tiehong. 2011. “A Minimal Volume Arithmetic Cusped Complex Hyperbolic Orbifold.” Mathematical Proceedings of the Cambridge Philosophical Society 150 (2): 313–342. doi:10.1017/S0305004110000526.
books
- Goldman, William M. 1999. Complex Hyperbolic Geometry. Oxford Mathematical Monographs. New York: The Clarendon Press Oxford University Press. http://www.ams.org/mathscinet-getitem?mr=1695450.
- complex Kleinian groups
expositions
- Traces in complex hyperbolic geometry
- Parker, John R. 2009. “Complex Hyperbolic Lattices.” In Discrete Groups and Geometric Structures, 501:1–42. Contemp. Math. Providence, RI: Amer. Math. Soc. http://www.ams.org/mathscinet-getitem?mr=2581913.
articles
- Parker, John R. 1998. “On the Volumes of Cusped, Complex Hyperbolic Manifolds and Orbifolds.” Duke Mathematical Journal 94 (3): 433–464. doi:10.1215/S0012-7094-98-09418-2.
- Hersonsky, Sa’ar, and Frédéric Paulin. 1996. “On the Volumes of Complex Hyperbolic Manifolds.” Duke Mathematical Journal 84 (3): 719–737. doi:10.1215/S0012-7094-96-08422-7.