2 problems

Let $-\infty\leq\kappa_1<\kappa_2\leq+\infty$ and $-\infty\leq\bar\kappa_1<\bar\kappa_2\leq+\infty$. Let $\mathscr{L}_{\kappa_1}^{\kappa_2}$ and…

Let $I$ be the parameter interval, and let $\mathscr{L}_{\kappa_1}^{\kappa_2}(I)$ be the space of curves on $\mathbf{S}^2$ with geodesic curvature in $(\kappa_1,\kappa_2)$, while…