Geodesic nets on non-compact Riemannian manifolds

Autor:	Chambers, Gregory R., Liokumovich, Yevgeny, Nabutovsky, Alexander, Rotman, Regina
Rok vydání:	2022
Předmět:	Mathematics - Differential Geometry Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	A geodesic flower is a finite collection of geodesic loops based at the same point $p$ that satisfy the following balancing condition: The sum of all unit tangent vectors to all geodesic arcs meeting at $p$ is equal to the zero vector. In particular, a geodesic flower is a stationary geodesic net. We prove that in every complete non-compact manifold with locally convex ends there exists a non-trivial geodesic flower.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2205.09242 Zobrazit plný text záznamu View this record from Arxiv