2023-04-142023-04-142021-01-26Kohlenbach, U.W., López Acedo, G. y Nicolae, A. (2021). A uniform betweenness property in metric spaces and its role in the quantitative analysis of the “Lion-man” game. Pacific Journal of Mathematics, 310 (1), 181-212. https://doi.org/10.2140/pjm.2021.310.181.1945-58440030-8730https://hdl.handle.net/11441/144354We 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.application/pdf31 p.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/lion and man gamerate of convergenceuniform convexitybetweenness propertyinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/embargoedAccess10.2140/pjm.2021.310.181