Faculté des sciences

Découpages et inégalités systoliques pour les surfaces hyperboliques

Gendulphe, Matthieu

In: Geometriae Dedicata, 2009, vol. 142, no. 1, p. 23-35

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. Plus

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    Summary
    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.