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On the volumes of canonical cusps of complex hyperbolic manifolds
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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.
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.
참고문헌 (6)
- W. M. Goldman, "Complex Hyperbolic Geometry, Oxford Mathematical Monographs. Oxford Science Publications" (1999), The Clarendon Press, Oxford University Press
- S. Hersonsky, "On the volumes of complex hyperbolic manifolds", Duke Math. J., 84(3), pp.719~737 (1996)
- J.-M. Hwang, "On the volumes of complex hyperbolic manifolds with cusps", Internat. J. Math., 15(6), pp.567~572 (2004)
- B. Maskit, "Kleinian Groups", Grundlehren der Mathematischen Wissenschaften, 287 (1988), Springer-Verlag
- J. R. Parker, "On the volumes of cusped, complex hyperbolic manifolds and orbifolds", Duke Math. J., 94(3), pp.433~464 (1998)
- W. Thurston, "The geometry and topology of 3-manifolds", ~ (1991)
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