A non-compact convex hull in generalized non-positive curvature
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909373972873216 |
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| author | Basso, Giuliano Krifka, Yannick Soultanis, Elefterios |
| author_facet | Basso, Giuliano Krifka, Yannick Soultanis, Elefterios |
| contents | In this article, we are interested in metric spaces that satisfy a weak non-positive curvature condition in the sense that they admit a conical geodesic bicombing. We show that the analog of a question of Gromov about compactness properties of convex hulls has a negative answer in this setting. Specifically, we prove that there exists a complete metric space $X$ that admits a conical bicombing $σ$ such that $X$ has a finite subset whose closed $σ$-convex hull is not compact. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_03835 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A non-compact convex hull in generalized non-positive curvature Basso, Giuliano Krifka, Yannick Soultanis, Elefterios Metric Geometry Differential Geometry Geometric Topology 53C23 (Primary) 51F99 (Secondary) In this article, we are interested in metric spaces that satisfy a weak non-positive curvature condition in the sense that they admit a conical geodesic bicombing. We show that the analog of a question of Gromov about compactness properties of convex hulls has a negative answer in this setting. Specifically, we prove that there exists a complete metric space $X$ that admits a conical bicombing $σ$ such that $X$ has a finite subset whose closed $σ$-convex hull is not compact. |
| title | A non-compact convex hull in generalized non-positive curvature |
| topic | Metric Geometry Differential Geometry Geometric Topology 53C23 (Primary) 51F99 (Secondary) |
| url | https://arxiv.org/abs/2301.03835 |