On a Conjecture of Harvey and Lawson
Complex Variables
2008-07-24 v1 Differential Geometry
Abstract
We consider complex projective space P^{n} and a smooth closed curve gamma in P^{n}. Harvey and Lawson have defined the notion of the projective hull \hat{K} of a compact subset K in P^n. This concept is an analogue of the polynomial hull of compact subsets of C^{n}. In the present note we study the relation between the following two properties of the curve gamma: (1) \hat{gamma} - gamma is a one-dimensional complex analytic subvariety of P^{n} - gamma, and (2) There exists a Stein subdomain of P^{n} which contains the projective hull \hat{gamma} of gamma.
Cite
@article{arxiv.0807.3583,
title = {On a Conjecture of Harvey and Lawson},
author = {John Wermer},
journal= {arXiv preprint arXiv:0807.3583},
year = {2008}
}