Geodesic complexity for non-geodesic spaces

2020/09/24 by Davis, Donald M.
#53C22 #55M30 #55R80 #68T40 #Algebraic Topology (math.AT) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2009.11628

Abstract

We define the notion of near geodesic between points of a metric space when no geodesic exists, and use this to extend Recio-Mitter's notion of geodesic complexity to non-geodesic spaces. This has potential application to topological robotics. We determine explicit near geodesics and geodesic complexity in a variety of cases.

Related

• Geodesic complexity of a cube
• The geodesic complexity of n-dimensional Klein bottles
• Geodesic complexity of a tetrahedron
• Complexity of Bezout's Theorem VI: Geodesics in the Condition (Number) Metric
• Point-assigned distance-like functions on non-compact geodesic spaces