On Almost-Fuchsian submanifodls of Hadamard spaces and the asymptotic Plateau problem
Abstract
We consider minimal submanifolds of negatively curved spaces with small curvature. We show that in a Hadamard space with negatively pinched curvature -C≤ K≤ -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.
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