caa a22 4500 445837039 CHVBK 20180317145333.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s00209-010-0749-7 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0749-7 Rotman Regina Department of Mathematics, University of Toronto, M5S 2E4, Toronto, ON, Canada aut Flowers on Riemannian manifolds [Elektronische Daten] [Regina Rotman] 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 M n 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 M n. We also show that there exists a minimal geodesic net that consists of one vertex and at most $${3^{(n+1)^2}}$$ loops of total length $${\leq2 (n+1)!^2 3^{(n+1)^3}\,Fill\,Rad\,M^n \leq2(n+1)!^{\frac{5}{2}}3^{(n+1)^3}(n+1)n^n vol(M^n)^{\frac{1}{n}}}$$, where FillRadM n denotes the filling radius and vol(M n) denotes the volume of M n. Springer-Verlag, 2010 Mathematische Zeitschrift Springer-Verlag 269/1-2(2011-10-01), 543-554 0025-5874 269:1-2<543 2011 269 209 https://doi.org/10.1007/s00209-010-0749-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0749-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Rotman Regina Department of Mathematics, University of Toronto, M5S 2E4, Toronto, ON, Canada aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 269/1-2(2011-10-01), 543-554 0025-5874 269:1-2<543 2011 269 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer