Geodesic rays, the "Lion-Man" game, and the fixed point property

2019/05/20 by López-Acedo, Genaro, Nicolae, Adriana, Piątek, Bożena
#FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1905.08334

Abstract

This paper focuses on the relation among the existence of different types of curves (such as directional ones, quasi-geodesic or geodesic rays), the (approximate) fixed point property for nonexpansive mappings, and a discrete lion and man game. Our main result holds in the setting of CAT(0) spaces that are additionally Gromov hyperbolic.

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