Flowers on Riemannian manifolds
نویسنده
چکیده
In this paper we will present two upper bounds for the length of a smallest “flower-shaped” geodesic net in terms of the volume and the diameter of a manifold. Minimal geodesic nets are critical points of the length functional on the space of graphs immersed into a Riemannian manifold. Let Mn be a closed Riemannian manifold of dimension n. We prove that there exists a minimal geodesic net that consists of one vertex and at most 2n− 1 geodesic loops based at that vertex of total length ≤ 2n!d, where d is the diameter of Mn. We also show that there exists a minimal geodesic net that consists of one vertex and at most 3 2 loops of total length ≤ 2(n + 1)!3 3 FillRadMn ≤
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تاریخ انتشار 2008