有界凸平衡域上的双全纯凸映照的判别准则

Criteria for Biholomorphic Convex Mappings on Bounded Convex Balanced Domains

本文讨论Cn中有界强凸平衡域和凸平衡域上局部双全纯映照成为双全纯凸映照的充要条件,从而得到Reinhardt域Dp= 上双全纯凸映照的充要条件,其中Pj≥2(j=1,2,…,n).

In this paper, we discuss the sufficient and necessary conditions that lo-cally biholomorphic mappings from a bounded strongly convex balanced domain or a bounded convex balanced domain into Cn be biholomorphic convex mappings. We also obtain the sufficient and necessary conditions for f to be biholomorphic convex on Reinhardt domains Dp = , where .