Bending deformations of complex hyperbolic surfaces

Journal fur die Reine und Angewandte Mathematik

Volumn 492, Issue , 1997, Pages 75-91

  Apanasov, Boris ^a,b  

^a UNIVERSITY OF OKLAHOMA   (United States)

^b MATHEMATICAL SCIENCES RESEARCH INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031537147     PISSN: 00754102     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (49)

1. Boris Apanasov, Discrete groups in Space and Uniformization Problems, Math. Appl. 40, Kluwer Academic Publishers, Dordrecht 1991.
2. Boris Apanasov, Nontriviality of Teichmüller space for Kleinian group in space, Riemann Surfaces and Related Topics: Proc. 1978 Stony Brook Conference (I. Kra and B. Maskit, eds.), Ann. Math. Stud. 97, Princeton Univ. Press (1981), 21-31.
3. Boris Apanasov, Thurston's bends and geometric deformations of conformal structures, Complex Analysis and Applications '85, Publ. Bulgarian Acad. Sci., Sofia (1986), 14-28.
4. Boris Apanasov, Deformations of conformal structures on hyperbolic manifolds, J. Diff. Geom. 35 (1992), 1-20.
5. Boris Apanasov, Conformal geometry of discrete groups and manifolds, W. de Gruyter, Berlin-New York, to appear.
6. Boris Apanasov, Canonical homeomorphisms in Heisenberg groups induced by isomorphisms of discrete subgroups of PU(n, 1), Russian Acad. Sci. Dokl. Math. 356 (1997), to appear.
7. Boris Apanasov, Quasiconformality and geometrical finiteness in Carnot-Carathéodory and negatively curved spaces, Geometry, Topology and Physics, W. de Gruyter, Berlin - New York (1997), 25-44.
8. Boris Apanasov, Geometry and topology of complex hyperbolic and CR-manifolds, Russian Math. Surv. 52:5 (1997), to appear.
9. Boris Apanasov, Mario Carneiro and Nikolay Gusevskii, Some deformations of complex hyperbolic surfaces, in preparation.
10. Boris Apanasov and Nikolay Gusevskii, The boundary of Teichmüller space of complex hyperbolic surfaces, in preparation.
11. Boris Apanasov and Xiangdong Xie, Geometrically finite complex hyperbolic manifolds, Intern. J. Math., to appear.
12. Boris Apanasov and Xiangdong Xie, Manifolds of negative curvature and nilpotent groups, Complex Analysis, Differential Geometry and Mathematical Physics (Proc. of the third Intern. Workshop at Varna, K. Sekigawa and S. Dimiev, eds.), World Scientific, Singapore (1997), 105-115.
13. Boris Apanasov and Xiangdong Xie, Discrete actions on nilpotent groups and negatively curved spaces, preprint, Univ. of Tokyo, 1997.
14. A. F. Beardon, The geometry of discrete groups, Springer-Verlag, Berlin - New York 1983.
15. D. Burns and S. Shnider, Spherical hypersurfaces in complex manifolds, Inv. Math. 33 (1976), 223-246.
16. Peter Buser, The collar theorem and examples, Manuscr. Math. 25 (1978), 349-357.
17. Mario Carneiro and Nicolay Gusevskii, Some deformations of complex hyperbolic surfaces, in preparation.
18. Élie Cartan, Sur le groupe de la géométrie hypersphérique, Comm. Math. Helv. 4 (1932), 158-171.
19. S. Chen and L. Greenberg, Hyperbolic spaces, Contributions to Analysis, Academic Press, New York (1974), 49-87.
20. Kevin Corlette, Archimedian superrigidity and hyperbolic geometry, Ann. Math. 135 (1992), 165-182.
21. J. Cygan, Wiener's test for Brownian motion on the Heisenberg group, Colloqu. Math. 39 (1978), 367-373.
22. Elisha Falbel and Nikolay Gusevskii, Spherical CR-manifolds of dimension 3, Bol. Soc. Bras. Mat. 25 (1994), 31-56.
23. William Goldman, Representations of fundamental groups of surfaces, Geometry and topology (J. Alexander and J. Harer, eds.), Springer, Lect. Notes Math. 1167 (1985), 95-117.
24. William Goldman, Geometric structures on manifolds and varieties of representations, Geometry of Group Representations (A. Magid and W. Goldman, eds.), Contemp. Math. 74 (1988), 169-198.
25. William Goldman, Complex hyperbolic Kleinian groups, Complex geometry, Lect. Notes Pure Appl. Math. 143 (1993), 31-52.
26. William Goldman, Complex hyperbolic geometry, Oxford Univ. Press, to appear.
27. W. Goldmanm M. Kapovich and B. Leeb, Complex hyperbolic manifolds homotopy equivalent to a Riemann surface, Preprint 1995.
28. William Goldman and John Millson, Local rigidity of discrete groups acting on complex hyperbolic space, Invent. Math. 88 (1987), 495-520.
29. William Goldman and John Parker, Complex hyperbolic ideal triangle groups, J. reine angew. Math. 425 (1992), 71-86.
30. Nikolay Gusevskii, Colloquium talk, Univ. of Oklahoma, Norman, December 1995.
31. Dennis Johnson and John Millson, Deformation spaces associated to compact hyperbolic manifolds, Discrete Groups in Geometry and Analysis: Papers in Honor of G. D. Mostow on His Sixtieth Birthday, Ed. R. Howe, Birkhäuser, Boston (1987), 48-106.
32. Linda Keen, Collars on Riemann surfaces, Discontinuous groups and Riemann surfaces, Ann. Math. Stud. 79, Princeton Univ. Press (1974), 263-268.
33. Adam Koranyi and Martin Reimann, Quasiconformal mappings on the Heisenberg group, Invent. Math. 80 (1985), 309-338.
34. Adam Koranyi and Martin Reimann, Equivariant extension of quasiconformal deformations into complex bal, preprint 1996.
35. Christos Kourouniotis, Deformations of hyperbolic structures, Math. Proc. Cambr. Phil. Soc. 98 (1985), 247-261.
36. Georgii A. Margulis, Discrete groups of motions of manifolds of non-positive curvature, Proc. ICM, Vancouver 2 (1974), 21-34 (Russian); Engl. Transl.: Amer. Math. Soc. Transl. 109 (1977), 33-45.
37. Georgii A. Margulis, Discrete groups of motions of manifolds of non-positive curvature, Proc. ICM, Vancouver 2 (1974), 21-34 (Russian); Engl. Transl.: Amer. Math. Soc. Transl. 109 (1977), 33-45.
38. Bernard Maskit, Kleinian groups, Springer-Verlag, 1987.
39. George D. Mostow, Strong rigidity of locally symmetric spaces, Princeton Univ. Press, 1973.
40. George D. Mostow, On a remarkable class of polyhedra in complex hyperbolic space, Pacific J. Math. 86 (1980), 171-276.
41. Pierre Pansu, Métriques de Carnot-Carathéodory et quasiisométries des espaces symmétries de rang un, Ann. Math. 129 (1989), 1-60.
42. John Parker, Shimizu's lemma for complex hyperbolic space, Intern. J. Math. 3 : 2 (1992), 291-308.
43. Dennis Sullivan, Quasiconformal homeomorphisms and dynamics, II: Structural stability implies hyperbolicity for Kleinian groups, Acta Math. 155 (1985), 243-260.
44. William Thurston, The geometry and topology of three-manifolds, Lect. Notes, Princeton Univ., 1981.
45. Domingo Toledo, Representations of surface groups on complex hyperbolic space, J. Diff. Geom. 29 (1989), 125-133.
46. Pekka Tukia, On isomorphisms of geometrically finite Kleinian groups, Publ. Math. IHES 61 (1985), 171-214.
47. A. Weil, Remarks on the cohomology of groups, Ann. Math. 80 (1964), 149-157.
48. S. T. Yau, Calabi's conjecture and some new results in algebraic geometry, Proc. Nat. Acad. Sci. 74 (1977), 1798-1799.
49. Chengbo Yue, Dimension and rigidity of quasi-Fuchsian representations, Ann. Math. 143 (1996), 331-355.