تقرير
A uniform betweenness property in metric spaces and its role in the quantitative analysis of the 'Lion-Man' game
| العنوان: | A uniform betweenness property in metric spaces and its role in the quantitative analysis of the 'Lion-Man' game |
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| المؤلفون: | Kohlenbach, Ulrich, López-Acedo, Genaro, Nicolae, Adriana |
| سنة النشر: | 2018 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Metric Geometry, Mathematics - Optimization and Control |
| الوصف: | In this paper we analyze, based on an interplay between ideas and techniques from logic and geometric analysis, a pursuit-evasion game. More precisely, we focus on a uniform betweenness property and use it in the study of a discrete lion and man game with an $\varepsilon$-capture criterion. In particular, we prove that in uniformly convex bounded domains the lion always wins and, using ideas stemming from proof mining, we extract a uniform rate of convergence for the successive distances between the lion and the man. As a byproduct of our analysis, we study the relation among different convexity properties in the setting of geodesic spaces. Comment: Change of title. Minor revision |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1806.04496 |
| رقم الأكسشن: | edsarx.1806.04496 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |