Sur la systole de la sphère au voisinage de la métrique standard
Balacheff, Florent Nicolas (Université de Genève. Section de Mathématiques)

Additional title:	On the systole of the sphere in the proximity of the standard metric
Date:	2006
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, admits the standard metric g 0 as a critical point, although it does 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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Language:	Francès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	2-sphere ; Critical point ; Standard metric ; Systole ; Zoll metric
Published in:	Geometriae dedicata (Dordrecht), Vol. 121, Issue 1 (August 2006) , p. 61-71, ISSN 1572-9168

DOI: 10.1007/s10711-006-9087-7

Postprint 12 p, 490.1 KB

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