Skip to main content
SpringerLink
Log in

Area growth and Green's function of Riemann surfaces

  • Published:
Arkiv för Matematik

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Ahlfors, L. V. andSario, L.,Riemann surfaces, Princeton University Press, Princeton, 1960.

    MATH  Google Scholar 

  2. Beardon, A. F.,The geometry of discrete groups, Springer-Verlag, New York, 1983.

    MATH  Google Scholar 

  3. Buser, P., Cubic graphs and the first eigenvalue of a Riemann surface,Math, Z.,162 (1978), 87–99.

    Article  MATH  MathSciNet  Google Scholar 

  4. Chavel, I.,Eigenvalues in Riemannian geometry, Academic Press, Orlando, Fla., 1984.

    MATH  Google Scholar 

  5. Doyle, P. G., Random walk on the Speiser graph of a Riemann surface,Bull. Amer. Math. Soc.,11 (1984), 371–377.

    Article  MATH  MathSciNet  Google Scholar 

  6. Doyle, P. G. andSnell, J. L.,Random walks and electric networks, Carus Mathematical Monographs, M.A.A., Washington, D.C., 1984.

    MATH  Google Scholar 

  7. Epstein, C. L., Positive harmonic functions on Abelian covers,J. Functional Analysis,82 (1989), 303–315.

    Article  MATH  Google Scholar 

  8. Fernandez, J. L., On the existence of Green's function in Riemannian manifolds,Proc. Amer. Math. Soc.,96 (1986), 284–286.

    Article  MATH  MathSciNet  Google Scholar 

  9. Kanai, M., Rough isometries and the parabolicity of Riemannian manifolds,J. Math. Soc. Japan,38 (1986), 227–238.

    Article  MATH  MathSciNet  Google Scholar 

  10. Karp, L., Subharmonic functions, harmonic mappings and isometric immersions,Seminar on Differential Geometry, ed. S.-T. Yau, Annals of Mathematics Studes, Princeton U.P., 1982.

  11. Kra, I.,Automorphic forms and Kleinian groups, Benjamin, Reading, 1972.

    MATH  Google Scholar 

  12. Lyons, T. andSullivan, D., Function theory, Random Paths and Covering Spaces,J. Diff. Geom.,19 (1984), 299–323.

    MATH  MathSciNet  Google Scholar 

  13. Nicholls, P. J., Fundamental regions and the type problem for a Riemann surface,Math, Z.,174 (1980), 187–196.

    Article  MATH  MathSciNet  Google Scholar 

  14. Pommerenke, Ch., Uniformly perfect sets and the Poincaré metric,Arch. Math.,32 (1979), 192–199.

    Article  MATH  MathSciNet  Google Scholar 

  15. Pommerenke, Ch., On Fuchsian groups of accessible type,Ann. Acad. Scient. Fennica,7 (1982), 249–258.

    MATH  MathSciNet  Google Scholar 

  16. Sullivan, D., On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions,Riemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference, ed. I. Kra and B. Maskit, pp. 465–496 Annals of Mathematics Studies, Princeton U. P., Princeton, 1981.

    Google Scholar 

  17. Varopoulos, N. Th., Potential theory and diffusion on Riemannian manifolds, in:Conference in Harmonic Analysis in Honor of Anthony Zygmund, pp. 821–837 Wadsworth, Belmont, California, 1983.

    Google Scholar 

  18. Varopoulos, N. Th., Small time Gaussian estimates of heat diffusion kernels. Part I: The semigroup technique,Bull. Sc. Math.,113 (1989), 253–277.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Autonóma de Madrid, E-28049, Madrid, Spain

    J. L. Fernández & J. M. Rodríguez

Authors
  1. J. L. Fernández
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. M. Rodríguez
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported by a grant of the CICYT, Ministerio de Educación y Ciencia, Spain.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fernández, J.L., Rodríguez, J.M. Area growth and Green's function of Riemann surfaces. Ark. Mat. 30, 83–92 (1992). https://doi.org/10.1007/BF02384863

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02384863

Keywords

Search

Navigation