度量空间中的一致介数性质及其在“狮人”博弈定量分析中的作用
A uniform betweenness property in metric spaces and its role in the quantitative analysis of the "Lion-Man" game
摘要：
在本文中，我们分析的基础上，从逻辑和几何分析的思想和技术之间的相互作用，追逃对策。更准确地说，我们专注于一个统一的介数属性，并使用它在离散的狮子和人的游戏与$\varepsilon$捕获标准的研究。特别是，我们证明了在一致凸有界域的狮子总是赢，并使用来自证明挖掘的想法，我们提取了一个统一的收敛速率的连续距离之间的狮子和man.As我们的分析的副产品，我们研究了不同的凸性之间的关系设置的测地空间。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
