Degree and holomorphic extensions
复变函数
2007-05-23 v1
摘要
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.
引用
@article{arxiv.math/0606727,
title = {Degree and holomorphic extensions},
author = {Josip Globevnik},
journal= {arXiv preprint arXiv:math/0606727},
year = {2007}
}
备注
8 pages