A quantitative analysis of the “Lion-Man” game

Title: A quantitative analysis of the “Lion-Man” game
Abstract: 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 discrete lion and man game with an ε-capture criterion. 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.
Joint work with Genaro López-Acedo and Adriana Nicolae.

References:

[1] U. Kohlenbach, G. López-Acedo, A. Nicolae, A quantitative analysis of the “Lion-Man” game. arXiv:1806.04496 [math.MG], 2019. Submitted.