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

Translated title of the contribution: On the systole of the sphere in the proximity of the standard metric

Florent Balacheff*

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

11 Citations (Scopus)

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.

Translated title of the contributionOn the systole of the sphere in the proximity of the standard metric
Original languageFrench
Pages (from-to)61-71
Number of pages11
JournalGeometriae Dedicata
Volume121
Issue number1
DOIs
Publication statusPublished - Aug 2006

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