Rigidity for convex mappings of Reinhardt domains and its applications
Rigidity for convex mappings of Reinhardt domains and its applications
复制标题
Reinhardt域凸映射的刚性及其应用
DOI：
10.1007/s11425-017-9359-9
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Wang Jianfei
中科院分区：
文献类型：
--
作者：
Liu Taishun;Tang Xiaomin;Wang Jianfei
本文研究了Reinhardt域上双全纯凸映射的刚性及其在极值点上的应用。通过引入一种Scaling方法，我们精确地构造了许多在这个区域的边界上只有一个无限不连续的无界凸映射。我们还利用整函数的Kobayashi度量和Liouvile型定理给出了这类无界凸映射的刚性。作为应用，我们得到了这类正规化凸映射族的极值点的集合。我们的结果将凸映射和相关极值点的刚性从单位球推广到Reinhardt域。
In this paper, we investigate rigidity and its application to extreme points of biholomorphic convex mappings on Reinhardt domains. By introducing a version of the scaling method, we precisely construct many unbounded convex mappings with only one infinite discontinuity on the boundary of this domain. We also give a rigidity of these unbounded convex mappings via Kobayashi metric and Liouville-type theorem of entire functions. As an application we obtain a collection of extreme points for the class of normalized convex mappings. Our results extend both the rigidity of convex mappings and related extreme points from the unit ball to Reinhardt domains.