Remarks on the Alexander-Wermer Theorem for Curves

Details Remarks on the Alexander-Wermer Theorem for Curves Remarks on the Alexander-Wermer Theorem for Curves

2006-10-20

arxiv.org/abs/math/0610611v1

Mathematics

Complex Variables

Scientific paper

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.

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