单叶p-调和映射  

On p-harmonic Univalent Mappings

作　　者：乔金静[1,2] 王仙桃[2] 

机构地区：[1]河北大学数学与计算机学院,河北保定071002 [2]湖南师范大学数学与计算机科学学院,长沙410081

出　　处：《数学物理学报（A辑）》2012年第3期588-600,共13页Acta Mathematica Scientia

基　　金：国家自然科学基金(11071063)资助

摘　　要：主要目的是介绍两个p-调和映射类HS_p和HC_p及其相应的子类HS_p^0和H_p^0,同时研究这些类中映射的性质.首先,讨论了HS_p^0和HC_p^0中映射的几何性质.证明了在HS_p^0和HC_p^0中的映射下,单位圆盘的像域分别是星形的和凸的.其次,确定了HS_p^0、H_p^0、HS_p∩T_p和HC_p∩T_p的极值点,其中T_p表示具有非负系数的p-调和映射类.最后,证明了HC_p中映射邻域的存在性.In this paper, the main aim is to introduce two classes HSp and HCp of p-harmonic mappings together with their corresponding subclasses HSp0 and HCp0, and investigate the properties of the mappings in these classes. First, we discuss the geometric properties of mappings belonging to HSp0 and HCp0, respectively. We prove that the image domains of the unit disk D under the mappings in HSp0 （resp. HCp0） are starlike （resp. convex）. Secondly, extreme points for classes HSp0, HCp0, HSp∩Tp and HCp∩Tp are determined, where Tp denotes the set of all p-harmonic mappings with nonnegative coefficients. Finally, we establish the existence of the neighborhoods of mappings in HCp.

关 键 词：P -调和映射 星形性 凸性 极值点 邻域 

分 类 号：O174.5[理学—数学]