On the Space of $C^1$ Regular Curves on Sphere with Constrained Curvature

Cong Zhou

Let ${\mathcal{P}}_{{\kappa }_1}^{{\kappa }_2}(\mathbf{P},\mathbf{Q})$ denote the set of $C^1$ regular curves in the $2$-sphere ${\mathbb{S}}^2$ that start and end at given points with the co…