Holomorphic mappings preserving Minkowski functionals

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:409

Article

Kosinski, Lukasz

关键词: Minkowski functionals;    Balanced domains;    quasi-circular domains;    Open maps;    Proper holomorphic maps;   

DOI  :  10.1016/j.jmaa.2013.07.030

来源: Elsevier

【 摘 要 】

We show that the equality m(1)(f(x)) = m(2)(g(x)) for x in a neighborhood of a point a remains valid for all x provided that f and g are open holomorphic maps,f (a) = g (a) = 0 and m(1) m(2) are Minkowski functionals of bounded balanced domains. Moreover, a polynomial relation between f and g is obtained. As a consequence of our considerations we extend the main result of Berteloot and Patrizio (2000)[2] and we simplify its proof. We also show how to apply our results to quasi-balanced domains. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free