Mathematische Annalen

, Volume 350, Issue 4, pp 919–951 | Cite as

Constante de Bers en genre 2

Article

Abstract

We introduce a new tool, the contiguity graph, which enables us to determine the Bers’s constant in genus two.

Mathematics Subject Classification (2000)

30F45 30F60 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliographie

  1. 1.
    Bavard, C.: La Systole des Surfaces Hyperelliptiques. Prépublication de l’ENS Lyon no. 71, Juillet (1992)Google Scholar
  2. 2.
    Bavard C.: Disques extrémaux et surfaces modulaires. Ann. Fac. Sci. Toulouse Math. (6) 5(2), 191–202 (1996)MATHMathSciNetGoogle Scholar
  3. 3.
    Bavard C.: Systole et invariant d’Hermite. J. Reine Angew. Math. 482, 93–120 (1997)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Bavard C.: Anneaux extrémaux dans les surfaces de Riemann. Manuscripta Math. 117, 265–271 (2005)MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Bavard C.: Théorie de Voronoï géométrique. Propriétés de finitude pour les familles de réseaux et analogues. Bull. Soc. Math. France 133(2), 205–257 (2005)MATHMathSciNetGoogle Scholar
  6. 6.
    Bers, L.: Spaces of degenerating Riemann surfaces. In: Discontinuous groups and Riemann surfaces (Proceedings of Conference, University of Maryland, College Park, Md., 1973). Ann. of Math. Studies, No. 79, pp. 43–55. Princeton University Press (1974)Google Scholar
  7. 7.
    Böröczky K.: Packing of spheres in spaces of constant curvature. Acta Math. Acad. Sci. Hungar. 32(3–4), 243–261 (1978)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Buser, P.: Geometry and Spectra of Compact Riemann Surfaces, Progress in Mathematics, vol. 106. Birkhäuser, Switzerland (1992)Google Scholar
  9. 9.
    Buser P., Seppälä M.: Symmetric pants decompositions of Riemann surfaces. Duke Math. J. 67(1), 39–55 (1992)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Diestel, R.: Graph Theory, Graduate Texts in Mathematics, vol. 173, 4th edn. Springer, Berlin (2005)Google Scholar
  11. 11.
    Gendulphe, M.: Paysage systolique des surfaces hyperboliques compactes de caractéristique -1. disponible à http://matthieu.gendulphe.com
  12. 12.
    Mumford D.: A remark on Mahler’s compactness theorem. Proc. Amer. Math. Soc. 28, 289–294 (1971)MATHMathSciNetGoogle Scholar
  13. 13.
    Parlier, H.: On the geometry of simple closed geodesics. PhD thesis, EPFL (2004)Google Scholar
  14. 14.
    Parlier H.: Lengths of geodesics on Riemann surfaces with boundary. Ann. Acad. Sci. Fenn. Math. 30(2), 227–236 (2005)MATHMathSciNetGoogle Scholar
  15. 15.
    Schmutz P.: Riemann surfaces with shortest geodesic of maximal length. Geom. Funct. Anal. 3(6), 564–631 (1993)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Institut de Mathématiques de BordeauxUniversité Bordeaux 1BordeauxFrance
  2. 2.Département de MathématiquesUniversité de FribourgFribourg PérollesSwitzerland

Personalised recommendations