The Shortest Geodesic Flower on a Manifold with Locally Convex Ends and Finite Volume
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910213720768512 |
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| author | Beach, Isabel |
| author_facet | Beach, Isabel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12642 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Shortest Geodesic Flower on a Manifold with Locally Convex Ends and Finite Volume Beach, Isabel Differential Geometry 53C22 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. |
| title | The Shortest Geodesic Flower on a Manifold with Locally Convex Ends and Finite Volume |
| topic | Differential Geometry 53C22 |
| url | https://arxiv.org/abs/2605.12642 |