Holomorphic mappings preserving Minkowski functionals

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• 作者：?ukasz Kosi¨½ski
• 关键词：Minkowski functionals ; Balanced domains ; quasi-circular domains ; Open maps ; Proper holomorphic maps
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2014
• 出版时间：15 January, 2014
• 年：2014
• 卷：409
• 期：2
• 页码：643-648
• 全文大小：394 K

文摘

We show that the equality for in a neighborhood of a point remains valid for all provided that and are open holomorphic maps, and are Minkowski functionals of bounded balanced domains. Moreover, a polynomial relation between and is obtained.

As a consequence of our considerations we extend the main result of Berteloot and Patrizio (2000) and we simplify its proof.

We also show how to apply our results to quasi-balanced domains.