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arXiv · 2605.12642

The Shortest Geodesic Flower on a Manifold with Locally Convex Ends and Finite Volume

Isabel Beach
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Abstract

Suppose $M$ is a complete, non-compact $n$-dimensional Riemannian manifold with locally convex ends and finite volume. We prove that $M$ admits a non-trivial geodesic net with one vertex, at most $(n+2)(n+1)/2$ edges, and total length at most $$(n+2)(n+1)(n/2)\operatorname{vol}(M)^{1/n}.$$ This is a quantitative version of a result of G. R. Chambers, Y. Liokumovich, A. Nabutovsky and R. Rotman.

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Isabel Beach. 2026-05-12. The Shortest Geodesic Flower on a Manifold with Locally Convex Ends and Finite Volume. https://arxiv.org/abs/2605.12642

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