The Mathematical Intelligencer

, Volume 16, Issue 3, pp 11–19 | Cite as

Hyperbolic Geometry and Spaces of Riemann Surfaces

  • Linda Keen


Modulus Space Riemann Surface Hyperbolic Plane Kleinian Group Hyperbolic Geometry 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. Poincaré,Papers on Fuchsian Functions, translated by J. Stillwell, New York: Springer-Verlag (1985).CrossRefzbMATHGoogle Scholar
  2. 2.
    R. Fricke and F. Klein,Vorlesungen über die Theorie der automorphen Funktionen, New York: Johnson Reprint (1965), Vol. 2.Google Scholar
  3. 3.
    L. Ahlfors,Lectures on Quasiconformal Mappings, New York: Van Nostrand (1966).zbMATHGoogle Scholar
  4. 4.
    L. Bers, Finite dimensional Teichmüller spaces and generalizations,Bull. AMS (2) 5 (1972), 257–300.Google Scholar
  5. 5.
    W. Fenchel and J. Nielsen, Discrete groups, unpublished manuscript.Google Scholar
  6. 6.
    B. Maskit,Kleinian Groups, New York: Springer-Verlag (1987).CrossRefGoogle Scholar
  7. 7.
    L. Keen, Canonical polygons for finitely generated Fuchsian groups,Acta Math. 115 (1966), 1–16.CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    L. Keen, Intrinsic moduli on Riemann surfaces,Ann. Math. 84(3) (1966), 404–120.CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    L. Keen, On Fricke moduli,Advances in the Theory of Riemann Surfaces, Princeton, NJ: Princeton University Press (1971), 205–224.Google Scholar
  10. 10.
    W. P. Thurston, The geometry and topology of three- manifolds, unpublished manuscript.Google Scholar
  11. 11.
    F. Gardiner,Teichmüller Theory and Quadratic Differentials, New York: Wiley (1987).Google Scholar
  12. 12.
    D. J. Wright, The shape of the boundary of Maskit’s embedding of the Teichmüller space of once punctured tori, preprint.Google Scholar
  13. 13.
    L. Keen and C. Series, Pleating coordinates for the Maskit embedding of the Teicmüller space of punctured tori,Topology 32(4) (1993), 719–749.CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    L. Keen and C. Series, Pleating coordinates for the Teichmüller space of punctured tori,Bull. AMS. (2) 26 (1992), 141–146.CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    L. Keen and C. Series, The Riley slice of Schottky space (to appear).Google Scholar
  16. 16.
    L. Keen, B. Maskit, and C. Series, Geometric finiteness and uniqueness for Kleinian groups with circle-packing limit sets,J. Reine angew. Math. 436 (1993), 209–219.zbMATHMathSciNetGoogle Scholar
  17. 17.
    L. Keen, J. Parker, and C. Series, Pleating coordinates for the twice-punctured torus. In preparation.Google Scholar
  18. 18.
    L. Greenberg, Fundamental polyhedra for Kleinian groups.Ann. Math. 84(2) (1966), 433–441.CrossRefzbMATHGoogle Scholar
  19. 19.
    A. Marden, The geometry of finitely generated Kleinian groups,Ann. Math. 99 (1974), 383–462.CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    C. Series, The geometry of Markoff numbers,Math. Intelligencer 7(3) (1985), 20–29.CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 1994

Authors and Affiliations

  • Linda Keen
    • 1
  1. 1.Mathematics DepartmentCUNY Lehman CollegeBronxUSA

Personalised recommendations