Remarks on the Alexander-Wermer Theorem for Curves
Complex Variables
2017-12-12 v1 Differential Geometry
Abstract
We give a new proof of the Alexander-Wermer Theorem that characterizes the oriented curves in C^n which bound positive holomorphic chains, in terms of the linking numbers of the curve with algebraic cycles in the complement. In fact, we establish a slightly stronger version which applies to a wider class of boundary 1-cycles. Arguments here are based on the Hahn-Banach Theorem and some geometric measure theory. Several ingredients in the original proof have been eliminated.
Cite
@article{arxiv.math/0610611,
title = {Remarks on the Alexander-Wermer Theorem for Curves},
author = {F. Reese Harvey and H. Blaine Lawson},
journal= {arXiv preprint arXiv:math/0610611},
year = {2017}
}