Duke Mathematical Journal
previous :: next

On the volumes of cusped, complex hyperbolic manifolds and orbifolds

John R. Parker

Source: Duke Math. J. Volume 94, Number 3 (1998), 433-464.

First Page PDF: View first page of article (PDF, 105 KB)

Primary Subjects: 32H20
Secondary Subjects: 20H10, 57M50

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077230453
Mathematical Reviews number (MathSciNet): MR1639519
Zentralblatt MATH identifier: 0951.32019
Digital Object Identifier: doi:10.1215/S0012-7094-98-09418-2

References

[1] C. C. Adams, The noncompact hyperbolic $3$-manifold of minimal volume, Proc. Amer. Math. Soc. 100 (1987), no. 4, 601–606.
Mathematical Reviews (MathSciNet): MR88m:57018
Zentralblatt MATH: 0634.57008
Digital Object Identifier: doi:10.2307/2046691
[2] A. Basmajian and R. Miner, Discrete subgroups of complex hyperbolic motions, Invent. Math. 131 (1998), no. 1, 85–136.
Mathematical Reviews (MathSciNet): MR99e:32039
Zentralblatt MATH: 0901.32018
Digital Object Identifier: doi:10.1007/s002220050198
[3] M. Beals, C. Fefferman, and R. Grossman, Strictly pseudoconvex domains in $\mathbb{C}^{n}$, Bull. Amer. Math. Soc. (N.S.) 8 (1983), no. 2, 125–322.
Mathematical Reviews (MathSciNet): MR85a:32025
Zentralblatt MATH: 0546.32008
[4] K. Böröczky, Packing of spheres in spaces of constant curvature, Acta Math. Acad. Sci. Hungar. 32 (1978), no. 3-4, 243–261.
Mathematical Reviews (MathSciNet): MR80h:52014
Zentralblatt MATH: 0422.52011
Digital Object Identifier: doi:10.1007/BF01902361
[5] P. Buser and H. Karcher, Gromov's almost flat manifolds, Astérisque, vol. 81, Soc. Math. France, Paris, 1981.
Mathematical Reviews (MathSciNet): MR83m:53070
Zentralblatt MATH: 0459.53031
[6] J. Cygan, Wiener's test for the Brownian motion on the Heisenberg group, Colloq. Math. 39 (1978), no. 2, 367–373.
Mathematical Reviews (MathSciNet): MR82j:60153
Zentralblatt MATH: 0409.60075
[7] D. B. A. Epstein, Complex hyperbolic geometry, Analytical and Geometric Aspects of Hyperbolic Space (Coventry/Durham, 1984) ed. D. B. A. Epstein, London Math. Soc. Lecture Note Ser., vol. 111, Cambridge Univ. Press, Cambridge, 1987, pp. 93–111.
Mathematical Reviews (MathSciNet): MR89c:32082
Zentralblatt MATH: 0611.51012
[8] J.-M. Feustel, Kompaktifizierung und Singularitäten des Faktorraumes einer arithmetischen Gruppe, die in der zweidimensionalen Einheitskugel wirkt, Diplomarbeit, Humboldt University, Berlin, 1976.
[9] W. M. Goldman, Complex hyperbolic geometry, 1992, final preliminary version.
[10] W. M. Goldman and J. R. Parker, Dirichlet polyhedra for dihedral groups acting on complex hyperbolic space, J. Geom. Anal. 2 (1992), no. 6, 517–554.
Mathematical Reviews (MathSciNet): MR94d:32044
Zentralblatt MATH: 0762.51009
[11] S. Hersonsky, Covolume estimates for discrete groups of hyperbolic isometries having parabolic elements, Michigan Math. J. 40 (1993), no. 3, 467–475.
Mathematical Reviews (MathSciNet): MR94k:22023
Zentralblatt MATH: 0824.57024
Digital Object Identifier: doi:10.1307/mmj/1029004832
Project Euclid: euclid.mmj/1029004832
[12] S. Hersonsky and F. Paulin, On the volumes of complex hyperbolic manifolds, Duke Math. J. 84 (1996), no. 3, 719–737.
Mathematical Reviews (MathSciNet): MR97h:32036
Zentralblatt MATH: 0866.53036
Digital Object Identifier: doi:10.1215/S0012-7094-96-08422-7
Project Euclid: euclid.dmj/1077244041
[13] R.-P. Holzapfel, A class of minimal surfaces in the unknown region of surface geography, Math. Nachr. 98 (1980), 211–232.
Mathematical Reviews (MathSciNet): MR83a:14031
Zentralblatt MATH: 0474.14022
[14] R.-P. Holzapfel, Geometry and Arithmetic Around Euler Partial Differential Equations, Mathematics and its Applications (East European Series), vol. 11, Reidel, Dordrecht, 1986.
Mathematical Reviews (MathSciNet): MR88b:32075
Zentralblatt MATH: 0595.14016
[15] Y. Kamishima, Transformation groups on Heisenberg geometry, Kumamoto J. Math. 9 (1996), 53–64.
Mathematical Reviews (MathSciNet): MR97e:53046
Zentralblatt MATH: 0874.53021
[16] S. Kamiya, Notes on nondiscrete subgroups of $\hat {\rm U}(1,\,n;\,F)$, Hiroshima Math. J. 13 (1983), no. 3, 501–506.
Mathematical Reviews (MathSciNet): MR85f:20042
Zentralblatt MATH: 0542.22008
[17] S. Kamiya, Notes on elements of ${\rm U}(1,n;{\bf C})$, Hiroshima Math. J. 21 (1991), no. 1, 23–45.
Mathematical Reviews (MathSciNet): MR93e:22020b
Zentralblatt MATH: 0721.30033
[18] R. Meyerhoff, Sphere-packing and volume in hyperbolic $3$-space, Comment. Math. Helv. 61 (1986), no. 2, 271–278.
Mathematical Reviews (MathSciNet): MR88e:52023
Zentralblatt MATH: 0611.57010
[19] J. R. Parker, Shimizu's lemma for complex hyperbolic space, Internat. J. Math. 3 (1992), no. 2, 291–308.
Mathematical Reviews (MathSciNet): MR93a:32051
Zentralblatt MATH: 0761.32014
Digital Object Identifier: doi:10.1142/S0129167X92000096
[20] J. R. Parker, On Ford isometric spheres in complex hyperbolic space, Math. Proc. Cambridge Philos. Soc. 115 (1994), no. 3, 501–512.
Mathematical Reviews (MathSciNet): MR95g:51023
Zentralblatt MATH: 0819.32010
[21] J. R. Parker, Uniform discreteness and Heisenberg translations, Math. Z. 225 (1997), no. 3, 485–505.
Mathematical Reviews (MathSciNet): MR99f:32041
Zentralblatt MATH: 0881.32013
Digital Object Identifier: doi:10.1007/PL00004315
[22] H. Sandler, Trace equivalence in ${\rm SU}(2,1)$, Geom. Dedicata 69 (1998), no. 3, 317–327.
Mathematical Reviews (MathSciNet): MR2000c:32076
Zentralblatt MATH: 0894.22006
Digital Object Identifier: doi:10.1023/A:1005079615846
previous :: next

2010 © Duke University Press