3 problems

Let the geodesic complexity of a convex polyhedron mean the minimum number of sets needed to cover its geodesic motion-planning problem, so that a complexity of at most four means…

Let the geodesic complexity of a convex polyhedron mean the minimum number of sets needed to cover its geodesic motion-planning problem, so that a complexity of at least four means…

Let $M$ be a closed manifold of dimension at least $2$ that is not homeomorphic to $S^2$. A Riemannian metric on $M$ has the stated property when there exists $p\in M$ such that…