2006/01/12 by Florent Balacheff
Biochemistry, Genetics and Molecular Biology · Mathematics · #Dermatological and Skeletal Disorders #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #math.DS #msc:37C27 #msc:53B20
paper · pdf · doi:10.1007/s10711-006-9087-7
published as Geometriae Dedicata 121 (2006) 61-71 · 12 pages
arxiv created 2006/01/12 · openalex publication_date 2006/07/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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