Geodesic complexity of a cube
Metric Geometry
2023-08-09 v1 Computational Geometry
Abstract
The topological (resp. geodesic) complexity of a topological (resp. metric) space is roughly the smallest number of continuous rules required to choose paths (resp. shortest paths) between any points of the space. We prove that the geodesic complexity of a cube exceeds its topological complexity by exactly 2. The proof involves a careful analysis of cut loci of the cube.
Cite
@article{arxiv.2308.04316,
title = {Geodesic complexity of a cube},
author = {Donald M. Davis},
journal= {arXiv preprint arXiv:2308.04316},
year = {2023}
}