On Almost-Fuchsian submanifodls of Hadamard spaces and the asymptotic Plateau problem

We consider minimal submanifolds of negatively curved spaces with small curvature. We show that in a Hadamard space with negatively pinched curvature $-C\le K\le -1$, complete minimal submanifolds with second fundamental form less than $1$ everywhere bound a class of spheres at infinity for which the asymptotic Plateau problem is uniquely solvable.