Geodesic nets on non-compact Riemannian manifolds

2022/05/18 by Gregory R. Chambers, Yevgeny Liokumovich, Chambers, Gregory R. +5
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #History and Theory of Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2205.09242

openalex publication_date 2022/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

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.

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