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Geometriae Dedicata

, Volume 142, Issue 1, pp 23–35 | Cite as

Découpages et inégalités systoliques pour les surfaces hyperboliques à bord

  • Matthieu Gendulphe
Original Paper

Résumé

Semi-eutactic and perfect surfaces are hyperbolic surfaces which have particular variational properties related to the systole (Bavard, J. Reine. Angew. Math. 482, 93–120, 1997). We focus on these surfaces, and build a systolic cutting procedure to divide them into pieces of Euler-Poincaré characteristic 0, then we give bounds for the systole. We are mainly concerned with bordered surfaces.

Mathematics Subject Classification (2000)

30F45 30F60 

Mots-clé

Hyperbolic Surface Systole 

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Références

  1. 1.
    Akrout H.: Singularités topologiques des systoles généralisées. Topology 42(2), 291–308 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Bavard C.: La systole des surfaces hyperelliptiques. Prépublication de l’École Normale Supérieure de Lyon 71, 1–6 (1992)Google Scholar
  3. 3.
    Bavard C.: Systole et invariant d’Hermite. J. Reine. Angew. Math. 482, 93–120 (1997)zbMATHMathSciNetGoogle Scholar
  4. 4.
    Bavard C.: Anneaux extrémaux dans les surfaces de Riemann. Manuscripta. Math. 117(3), 265–271 (2005)zbMATHCrossRefMathSciNetGoogle 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)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Buser P., Sarnak P.: On the period matrix of a Riemann surface of large genus. Invent. Math. 117(1), 27–56 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Chabauty C.: Limite d’ensembles et géométrie des nombres. Bull. Soc. Math. France 78, 143–151 (1950)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Gendulphe, M.: Paysage systolique des surfaces hyperboliques compactes de caractéristique −1, soumis, disponible à http://matthieu.gendulphe.com
  9. 9.
    Katz M., Schaps M., Vishne U.: Logarithmic growth of systole of arithmetic Riemann surfaces along congruence subgroups. J. Differential Geom. 76(3), 399–422 (2007)zbMATHMathSciNetGoogle Scholar
  10. 10.
    Mumford D.: remark on Mahler’s compactness theorem. Proc. Amer. Math. Soc. 28, 289–294 (1971)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Parlier, H.: On the geometry of simple closed geodesics, Thèse, EPFL (2004)Google Scholar
  12. 12.
    Parlier H.: Lengths of geodesics on Riemann surfaces with boundary. Ann. Acad. Sci. Fenn. Math. 30(2), 227–236 (2005)zbMATHMathSciNetGoogle Scholar
  13. 13.
    Schmutz P.: Riemann surfaces with shortest geodesic of maximal length. Geom. Funct. Anal. 3(6), 564–631 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Schmutz P.: Congruence subgroups and maximal Riemann surfaces. J. Geom. Anal. 4(2), 207–218 (1994)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of MathematicsBar Ilan UniversityRamat GanIsraël
  2. 2.Département de MathématiquesUniversité de FribourgFribourg PérollesSwitzerland

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