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On the asymptotic Plateau problem in Cartan--Hadamard manifolds
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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.
Forward citations
Cited by 2 Pith papers
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Rigidity of the hyperbolic marked energy spectrum and entropy for $k$-surfaces
In negatively curved 3-manifolds, the marked p-energy spectrum and the modified energy entropy of k-surfaces are rigid: equality or asymptotic behavior forces the ambient curvature to be constant.
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Foliated Plateau problems, geometric rigidity and equidistribution of closed $k$-surfaces
A survey of foliated Plateau problems showing that area-entropy and marked-area-spectrum rigidity for k-surfaces mirror classical geodesic-flow rigidity.
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