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Hausdorff dimensions of limit sets I

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References

  1. Anderson, M.: The Dirichlet problem at infinity. J. Differ. Geom.18, 701–721 (1983)

    Google Scholar 

  2. Burns, D., Shnider, S.: Spherical hypersurfaces in complex manifolds. Invent. Math.33, 223–246 (1976)

    Google Scholar 

  3. Cheng, S.Y., Li, P., Yau, S.-T.: On the upper estimate of the heat kernel of a complete Riemannian manifold. Am. J. Math.103, 1021–1063 (1981)

    Google Scholar 

  4. Eberlein, P., O'Neill, B.: Visibility manifolds. Pac. J. Math.46, 45–109 (1973)

    Google Scholar 

  5. Epstein, C., Melrose, R., Mendoza, G.: Resolvent of the Laplacian on strictly pseudoconvex domains. Preprint

  6. Federer, H.: Geometric measure theory. Berlin, Heidelberg, New York: Springer 1969

    Google Scholar 

  7. Goldman, W.: Geometric structures on manifolds and varieties of representations. In: Geometry of group representations. Goldman, W., Magid, A. (eds.). Contemp. Math.74, 169–198 (1988)

  8. Goldman, W.: A user's guide to complex hyperbolic geometry. Notes in evolution

  9. Gromov, M.: Asymptotic geometry of homogeneous spaces. In: Differential geometry on homogeneous spaces. Rend. Semin. Math., Fasc. speciale (1983)

  10. Helgason, S.: Groups and geometric analysis. Pure and Applied Mathematics113 (1984)

  11. Karpelevic, F.: The geometry of geodesics and the eigenfunctions of the Beltrami-Laplace operator on symmetric spaces. Trans. Mosc. Math. Soc.14, 48–185 (1965)

    Google Scholar 

  12. Kostant, B.: On the existence and irreducibility of certain series of representations. Bull. AMS75, 627–642 (1969)

    Google Scholar 

  13. Kulkarni, R.: Conformal geometry in higher dimensions I. Bull. AMS81, 736–738 (1975)

    Google Scholar 

  14. Kulkarni, R.: On the principle of uniformization. J. Differ. Geom.13, 109–138 (1978)

    Google Scholar 

  15. Lohoué, N., Rychener, T.: Die Resolvente von Δ auf symmetrischen Räume vom nichtkompakten Typ. Commun. Math. Helv.57, 445–468 (1982)

    Google Scholar 

  16. Maskit, B.: Kleinian groups. Berlin, Heidelberg, New York: Springer 1988

    Google Scholar 

  17. Mitchell, J.: On Carnot-Carathéodory metrics. J. Differ. Geom.21, 35–45 (1985)

    Google Scholar 

  18. Mostow, G.: Strong rigidity of locally symmetric spaces. Ann. Math. Stud. 78 (1978)

  19. Pansu, P.: Une inégalité isopérimétrique sur le groupe de Heisenberg. C. R. Acad. Sci. Paris Sér. I,295, 127–130 (1982)

    Google Scholar 

  20. Pansu, P.: Métriques de Carnot-Carathéodory et quasi-isométries des espaces symétriques de rang un. Ann. Math.129, 1–60 (1989)

    Google Scholar 

  21. Pansu, P.: Thèse

  22. Patterson, S.: The limit set of a Fuchsian group. Acta Math.136, 241–273 (1976)

    Google Scholar 

  23. Phillips, R.S., Sarnak, P.: The Laplacian for domains in hyperbolic space and limit sets of Kléinian groups. Acta Math.155, 173–241 (1985)

    Google Scholar 

  24. Strichartz, R.: Analysis of the Laplacian on the complete Riemannian manifold. J. Funct. Anal.52, 48–79 (1983)

    Google Scholar 

  25. Strichartz, R.: Sub-Riemannian geometry. J. Differ. Geom.24, 221–263 (1986)

    Google Scholar 

  26. Sullivan, D.: The density at infinity of a group of hyperbolic motions. Publ. IHES50 171–202 (1979)

    Google Scholar 

  27. Sullivan, D.: Growth of positive harmonic functions and Kleinian group limit sets of zero planar measure and Hausdorff dimension 2. Geometry Seminar, Utrecht 1980. In: Lecture Notes in Mathematics (eds.) Looijenga, E., Siersma, D., Takens, F.. Berlin, Heidelberg, New York: Springer 1981, Vol. 894, pp. 127–144

    Google Scholar 

  28. Sullivan, D.: Related aspects of positivity in Riemannian geometry. J. Differ. Geom.25, 327–351 (1987)

    Google Scholar 

  29. Sullivan, D.: Related aspects of positivity: λ-potential theory on manifolds, lowest eigenstates, Hausdorff geometry, renormalized Markov processes.... In: Aspects of mathematics and its applications. Barroso, J.A., (ed.), pp. 747–779. Amsterdam: North-Holland 1986

    Google Scholar 

  30. Varopoulos, N.: Analysis on nilpotent groups. J. Funct. Anal.66, 406–431 (1986)

    Google Scholar 

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Oblatum 28-VIII-1989 & 7-II-1990

This work was partially supported by an NSF Postdoctoral Research Fellowship

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Corlette, K. Hausdorff dimensions of limit sets I. Invent Math 102, 521–541 (1990). https://doi.org/10.1007/BF01233439

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