Degree and holomorphic extensions

• Autores: Josip Globevnik
• Localización: Mathematical research letters, ISSN 1073-2780, Vol. 14, Nº 4, 2007, págs. 615-622
• Idioma: inglés
• DOI: 10.4310/mrl.2007.v14.n4.a6
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• Resumen

  • Let $D$ be a bounded convex domain in $\C^N,\ N\geq 2$. We prove that a continuous map $\Phi\colon\ bD\rightarrow\C^N$ extends holomorphically through $D$ if and only if for every polynomial map $P\colon\ \C^N\rightarrow\C^N$ such that $\Phi+P\not= 0$ on $bD$, the degree of $\Phi+P|bD$ is nonnegative. We also prove another such theorem for more general domains.