Flowers on Riemannian manifolds
type: Item
instance of: scholarly article
title: Flowers on Riemannian manifolds
zbMATH Open document ID: 1243.53076
author: Regina Rotman
published in: Mathematische Zeitschrift
publication date: 2011-10-25T00:00:00Z
review text: A \textit{minimal geodesic flower} is a bouquet of finitely many geodesic loops starting at the same point with the following property: The sum of the unit vectors at the base point tangent to all geodesic arcs directed from the base point equals zero. The author shows that on a compact Riemannian manifold of dimension \(n\) there exists a non-trivial geodesic flower consisting of at most \(2n-1\) geodesic loops. The total length of the flower is bounded from above by \(2 n! d,\) where \(d\) denotes the diameter. The work is a continuation of the author's work on \textit{geodesic nets.}
reviewed by: Hans-Bert Rademacher
Mathematics Subject Classification ID: 53C22
zbMATH DE Number: 5963459
zbMATH Keywords: minimal geodesic net
zbMATH Keywords: diameter
zbMATH Keywords: filling radius
zbMATH Keywords: minimal geodesic flower
MaRDI profile type: Publication
full work available at URL: s00209-010-0749-7
OpenAlex ID: W2078905101
Wikidata QID: Q115388791
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DOI: 10.1007/S00209-010-0749-7
description: scientific article; zbMATH DE number 5963459