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Sur la systole de la sphère au voisinage de la métrique standard

Florent Balacheff
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Abstract

We study the systolic area (defined as the ratio of the area over the square of the systole) of the 2-sphere endowed with a smooth riemannian metric as a function of this metric. This function, bounded from below by a positive constant over the space of metrics, have the standard metric $g\_0$ for critic point, although this one do not achieve the conjectured global minimum : we show that for each tangent direction to the space of metrics at $g\_0$, there exists a variation by metrics corresponding to this direction along which the systolic area can only increase

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Florent Balacheff. 2006-01-12. Sur la systole de la sphère au voisinage de la métrique standard. https://doi.org/10.1007/s10711-006-9087-7

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