Patterson-Sullivan measure and conformally flat metrics

Mathematische Zeitschrift

Volumn 225, Issue 1, 1997, Pages 115-131

  Nayatani, Shin ^a  

^a TOHOKU UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031285593     PISSN: 00255874     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00004301     Document Type: Article

References (21)

1. Ahlfors, L. V.: Möbius transformations in several dimensions. Lecture Notes, Minneapolis: University of Minnesota 1981
2. Apanasov, B. N.: Discrete groups in space and unformization problems, Mathematics and Its Applications, Soviet Series 40, Dordrecht: Kluwer Academic Publishers 1991
3. Apanasov, B. N.: Kobayashi conformal metric on manifolds, Chern-Simons and η-invariants. International J. Math. 2, 361-382 (1991)
4. Bourguignon, J. P.: Les variétés de dimension 4 à courbure harmonique et à signature non nulle sont d'Einstein. Invent. Math. 63, 263-286 (1981)
5. Cheeger, J., Gromoll, D.: On the structure of complete manifolds of nonnegative curvature. Ann. Math. 96, 413-433 (1972)
6. Izeki, H.: On the decomposition of conformally flat manifolds. J. Math. Soc. Japan 45, 105-119 (1993)
7. Kato, S., Nayatani, S.: Complete conformal metrics with prescribed scalar curvature on subdomains of a compact manifold. Nagoya Math. J. 132, 155-173 (1993)
8. Kobayashi, O.: Scalar curvature of a metric with unit volume. Math. Ann. 279, 253-265 (1987)
9. Kulkarni, R. S.: Conformal structures and Möbius structures. In: R. S. Kulkarni and U. Pinkall (eds.) Conformal Geometry. Aspects Math. E 12 1-39, Braunschweig: Vieweg 1988
10. Kulkarni, R. S., Pinkall, U.: A canonical metric for Möbius structures and its applications. Math. Z. 216, 89-129 (1994)
11. Lafontaine, J.: Conformal geometry from the Riemannian viewpoint. In: R. S. Kulkarni and U. Pinkall (eds.) Conformal Geometry. Aspects Math. E 12 65-92, Braunschweig: Vieweg 1988
12. Nicholls, P. J.: The ergodic theory of discrete groups. London Math. Soc. Lect. Notes Ser. 143, Cambridge: Cambridge University Press 1989
13. Patterson, S. J.: The limit set of a Fuchsian group. Acta Math. 136, 241-273 (1976)
14. Phillips, R. S., Sarnak, P.: The Laplacian for domains in hyperbolic space and limit sets of Kleinian groups. Acta Math. 155, 173-241 (1985)
15. Schoen, R., Yau, S.-T.: On the structure of manifolds with positive scalar curvature. Manuscripta Math. 28, 159-183 (1979)
16. Schoen, R., Yau, S.-T.: Conformally flat manifolds, Kleinian groups and scalar curvature. Invent. Math. 92, 47-71 (1988)
17. Sullivan, D.: The density at infinity of a discrete group of hyperbolic motions. I.H.E.S. Publ. Math. 50, 171-202 (1979)
18. Sullivan, D.: Entropy, Hausdorff measures old and new, and limit sets of geometrically finite Kleinian groups. Acta Math. 153, 259-277 (1984)
19. Tanno, S.: 4-dimensional conformally flat Kähler manifolds. Tôhoku Math. J. 24, 501-504 (1972)
20. Tukia, P.: On isomorphisms of geometrically finite Möbius groups. I.H.E.S. Publ. Math. 61, 171-214 (1985)
21. Wu, H.: The Bochner technique in differential geometry. Mathematical Reports 3, London: Harwood Academic-Publishers 1988