Geodesic nets on non-compact Riemannian manifolds
Differential Geometry
2022-05-20 v1 Analysis of PDEs
Abstract
A geodesic flower is a finite collection of geodesic loops based at the same point that satisfy the following balancing condition: The sum of all unit tangent vectors to all geodesic arcs meeting at 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.
Keywords
Cite
@article{arxiv.2205.09242,
title = {Geodesic nets on non-compact Riemannian manifolds},
author = {Gregory R. Chambers and Yevgeny Liokumovich and Alexander Nabutovsky and Regina Rotman},
journal= {arXiv preprint arXiv:2205.09242},
year = {2022}
}