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    Zhao, Tiehong 2012. New construction of fundamental domains for certain Mostow groups. Pacific Journal of Mathematics, Vol. 259, Issue. 1, p. 209.

  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 150, Issue 2
  • March 2011, pp. 313-342

A minimal volume arithmetic cusped complex hyperbolic orbifold

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  • Published online: 08 October 2010

The sister of Eisenstein–Picard modular group is described explicitly in [10], whose quotient is a noncompact arithmetic complex hyperbolic 2-orbifold of minimal volume (see [16]). We give a construction of a fundamental domain for this group. A presentation of that lattice can be obtained from that construction, which relates to one of Mostow's lattices.

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[1]M. Deraux , E. Falbel and J. Paupert New constructions of fundamental polyhedra in complex hyperbolic space. Acta Math. 194 (2005), no. 2, 155201.

[2]E. Falbel and J. R. Parker The Geometry of Eisenstein–Picard Modular Group. Duke Math. J. 131 (2006), no. 2, 249289.

[4]G. Francsics and P. Lax A semi-explicit fundamental domain for the Picard Modular Group in complex hyperbolic space. Contemp. Math. 368 (2005), 211226.

[8]R.-P. Holzapfel A class of minimal surfaces in the unknown region of surface geography. Math. Nachr. 98 (1980), 211232.

[9]G. D. Mostow On a remarkable class of polyhedra in complex hyperbolic space. Pacific J. Math. 86 (1980), 171276.

[10]J. R. Parker On the volumes of cusped, complex hyperbolic manifolds and orbifolds. Duke Math. J. 94 (1998), No. 3, 433464.

[11]J. R. Parker Complex hyperbolic lattices. Contemp. Math. 501 (2009), 142.

[12]J. R. Parker Cone metrics on the sphere and Livné's lattices. Acta Math. 196 (2006), 164.

[13]E. Picard Sur des formes quadratiques ternaires indéfinies indéterminées conjuguées et sur les fonctions hyperfuchsiennes correspondantes. Acta Math. 5 (1884), 121182.

[14]E. Picard Sur des fonctions de deux variables indépendentes analogues aux fonctions modulaires. Acta Math. 2 (1883), 114135.

[15]G. P. Scott The geometries of 3-manifolds. Bull. London Math. Soc. 15 (1983), 401487.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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