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arXiv · 2205.09242

Geodesic nets on non-compact Riemannian manifolds

Gregory R. Chambers·Yevgeny Liokumovich·Alexander Nabutovsky·Regina Rotman
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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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Gregory R. Chambers, Yevgeny Liokumovich, Alexander Nabutovsky, Regina Rotman. 2022-05-18. Geodesic nets on non-compact Riemannian manifolds. https://arxiv.org/abs/2205.09242

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