Geodesic Nets: Some Examples and Open Problems

Autor:	Nabutovsky, Alexander, Parsch, Fabian
Rok vydání:	2019
Předmět:	Mathematics - Metric Geometry Mathematics - Differential Geometry
Druh dokumentu:	Working Paper
Popis:	Geodesic nets on Riemannian manifolds form a natural class of stationary objects generalizing geodesics. Yet almost nothing is known about their classification or general properties even when the ambient Riemannian manifold is the Euclidean plane or the round $2$-sphere. In the first half of this paper we survey some results and open questions (old and new) about geodesic nets on Riemannian manifolds. Many of these open questions are about geodesic nets on the Euclidean plane. The second half contains a partial answer for one of these questions, namely, a description of a new infinite family of geodesic nets on the Euclidean plane with 14 boundary (or unbalanced) vertices and arbitrarily many inner (or balanced) vertices of degree $\geq 3$. Comment: 44 pages, 26 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1904.00483 Zobrazit plný text záznamu View this record from Arxiv