Complex hyperbolic geometry

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 \(8\pi^2/3\)

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.

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

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.

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.