English

Degree and holomorphic extensions

Complex Variables 2007-05-23 v1

Abstract

Let D be a bounded convex domain in C^N, N\geq 2. We prove that a continous map F from bD to C^N extends holomorphically through D if and only if for every polynomial map P from C^N to C^N such that F+P has no zero on bD, the degree of F+P|bD is nonnegative. We also prove another such theorem for more general domains.

Keywords

Cite

@article{arxiv.math/0606727,
  title  = {Degree and holomorphic extensions},
  author = {Josip Globevnik},
  journal= {arXiv preprint arXiv:math/0606727},
  year   = {2007}
}

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8 pages