3 problems

Existence conjecture. The energy $E^A(C)$ admits a minimum in the class $\mathbb{C}$ of homotopies connecting $c_0$ and $c_1$. The text states that existence of minimal geodesics f…

Let $I=[0,1]$, and let $C:I\to\mathbb{R}^n$ and $C_h:I\to\mathbb{R}^n$ be Lipschitz homotopies. Define the length functions … Assume that $l_h\to l$ uniformly and that…

Let $u,v\in UT\mathbb{H}^2$ and let $\kappa_1<\kappa_2$ with $(\kappa_1,\kappa_2)$ containing $[-1,1]$. Consider the canonical subspaces of $\mathcal{C}_{\kappa_1}^{\kappa_2}(u,v)$…