On the asymptotic Plateau problem in Cartan--Hadamard manifolds
Differential Geometry
2023-01-18 v5
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.
Keywords
Cite
@article{arxiv.2107.14670,
title = {On the asymptotic Plateau problem in Cartan--Hadamard manifolds},
author = {Graham Smith},
journal= {arXiv preprint arXiv:2107.14670},
year = {2023}
}
Comments
41 Pages, 6 Figures, 4 Appendices, Compiled with PDFTeX. Minor corrections to the introduction