English

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