تقرير
A non-compact convex hull in generalized non-positive curvature
| العنوان: | A non-compact convex hull in generalized non-positive curvature |
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| المؤلفون: | Basso, Giuliano, Krifka, Yannick, Soultanis, Elefterios |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Metric Geometry, Mathematics - Differential Geometry, Mathematics - Geometric Topology, 53C23 (Primary) 51F99 (Secondary) |
| الوصف: | 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 $\sigma$ such that $X$ has a finite subset whose closed $\sigma$-convex hull is not compact. Comment: v4: improved presentation and correction of some typos |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/s00208-024-02905-w |
| URL الوصول: | http://arxiv.org/abs/2301.03835 |
| رقم الأكسشن: | edsarx.2301.03835 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/s00208-024-02905-w |
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