2018/06/03 by Kohlenbach, Ulrich, López-Acedo, Genaro, Nicolae, Adriana
#FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.1806.04496
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 ε-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.