Degree and holomorphic extensions
Josip Globevnik
Abstract
Let D be a bounded convex domain in CN, N≥ 2. We prove that a continous map F from bD to CN extends holomorphically through D if and only if for every polynomial map P from CN to CN 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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