Degree and holomorphic extensions

Details Degree and holomorphic extensions Degree and holomorphic extensions

2006-06-28

arxiv.org/abs/math/0606727v1

Mathematics

Complex Variables

8 pages

Scientific paper

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.

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