Degree and holomorphic extensions
Globevnik, Josip
Original · EN
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.
English translation
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