Complex Plateau problem: old and new results and prospects
Complex Variables
2011-05-24 v1
Abstract
The complex Plateau problem is analogous, in a Hermitian complex manifold, to the classical Plateau problem in 3 dimensional real space: it is a geometrical problem of extension of a closed real manifold into a complex analytic subvariety, or into a Levi-flat subvariety. Minimality of complex analytic subvarieties and analogous properties of Levi-flat subvarieties, in K\"ahler manifolds, are recalled or given. Known results in n dimensional complex and projective complex spaces are recalled. Extensions to real parametric problems are solved or proposed, leading to the construction of Levi-flat hypersurfaces with prescribed boundary in some complex manifolds.
Cite
@article{arxiv.1105.4417,
title = {Complex Plateau problem: old and new results and prospects},
author = {Pierre Dolbeault},
journal= {arXiv preprint arXiv:1105.4417},
year = {2011}
}