On the asymptotic Plateau problem in Cartan--Hadamard manifolds
arXiv:2107.14670
Abstract
We prove dynamical stability of a natural class of hypersurface laminations defined over Cartan--Hadamard manifolds of pinched curvature. We achieve this by providing a complete solution to the asymptotic Plateau problem for immersed surfaces of constant extrinsic curvature in Cartan--Hadamard manifolds, proposed by Labourie in [25], together with its natural higher-dimensional generalisation.
41 Pages, 6 Figures, 4 Appendices, Compiled with PDFTeX. Minor corrections to the introduction