Degree and holomorphic extensions

Josip Globevnik

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arXiv · math/0606727

Degree and holomorphic extensions

Josip Globevnik

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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.

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Josip Globevnik. 2006-06-28. Degree and holomorphic extensions. https://arxiv.org/abs/math/0606727

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