Homotopies of Curves on the 2-Sphere with Geodesic Curvature in a Prescribed Interval

Pedro Zühlke

Let $C_{k_1}^{k_2}$ denote the set of all closed curves of class $C^r$ on the sphere $S^2$ whose geodesic curvatures are restricted to lie in $(k_1,k_2)$, furnished with the $C^r$…