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Découpages et inégalités systoliques pour les surfaces hyperboliques à bord

Gendulphe, Matthieu

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

The homology systole of hyperbolic Riemann surfaces

Parlier, Hugo

In: Geometriae Dedicata, 2012, vol. 157, no. 1, p. 331-338

(On the systole of the sphere in the proximity of the standard metric) = Sur la systole de la sphère au voisinage de la métrique standard

Balacheff, Florent

In: Geometriae Dedicata, 2006, vol. 121, no. 1, p. 61-71

The homology systole of hyperbolic Riemann surfaces

Parlier, Hugo

In: Geometriae Dedicata, 2012, vol. 157, no. 1, p. 331-338

The main goal of this note is to show that the study of closed hyperbolic surfaces with maximum length systole is in fact the study of surfaces with maximum length homological systole. The same result is shown to be true for once-punctured surfaces, and is shown to fail for surfaces with a large number of cusps.

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...