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. |
Rights: |
Tots els drets reservats. |
Language: |
Francès |
Document: |
Article ; recerca ; Versió acceptada per publicar |
Subject: |
2-sphere ;
Critical point ;
Standard metric ;
Systole ;
Zoll metric |
Published in: |
Geometriae Dedicata, Vol. 121, Issue 1 (August 2006) , p. 61-71, ISSN 1572-9168 |
DOI: 10.1007/s10711-006-9087-7
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Record created 2024-01-23, last modified 2024-05-04