Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON THE VOLUMES OF CANONICAL CUSPS OF COMPLEX HYPERBOLIC MANIFOLDS

  • Kim, In-Kang (DEPARTMENT OF MATHEMATICS SEOUL NATIONAL UNIVERSITY) ;
  • Kim, Joon-Hyung (DEPARTMENT OF MATHEMATICS SEOUL NATIONAL UNIVERSITY)
  • Published : 2009.05.01
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Abstract

We first introduce a complex hyperbolic space and a complex hyperbolic manifold. After defining the canonical horoball and the canonical cusp on the complex hyperbolic manifold, we estimate the volumes of canonical cusps of complex hyperbolic manifolds. Finally, we deal with cusped, complex hyperbolic 2-manifolds, and in particular, the ones with only one cusp.

Keywords

References

  1. W. M. Goldman, Complex Hyperbolic Geometry, Oxford Mathematical Monographs. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1999
  2. S. Hersonsky and F. Paulin, On the volumes of complex hyperbolic manifolds, Duke Math. J. 84 (1996), no. 3, 719–737 https://doi.org/10.1215/S0012-7094-96-08422-7
  3. J.-M. Hwang, On the volumes of complex hyperbolic manifolds with cusps, Internat. J. Math. 15 (2004), no. 6, 567–572
  4. B. Maskit, Kleinian Groups, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 287. Springer-Verlag, Berlin, 1988
  5. J. R. Parker, On the volumes of cusped, complex hyperbolic manifolds and orbifolds, Duke Math. J. 94 (1998), no. 3, 433–464 https://doi.org/10.1215/S0012-7094-98-09418-2
  6. W. Thurston, The geometry and topology of 3-manifolds, preprint, 1991

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