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arXiv · 1806.04496

A uniform betweenness property in metric spaces and its role in the quantitative analysis of the "Lion-Man" game

Ulrich Kohlenbach·Genaro López-Acedo·Adriana Nicolae
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Abstract

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.

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Ulrich Kohlenbach, Genaro López-Acedo, Adriana Nicolae. 2018-06-03. A uniform betweenness property in metric spaces and its role in the quantitative analysis of the "Lion-Man" game. https://arxiv.org/abs/1806.04496

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