Hyperbolic linear invariance and hyperbolic k-convexity

Journal of the Australian Mathematical Society

Wancang Ma¹ 

[1] David Minda

关键词: 30C99;    30C25;    30C45;    30D45;   

DOI  :  10.1017/S1446788700038118

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Pommerenke initiated the study of linearly invariant families of locally schlicht holomorphic functions defined on the unit diskThe concept of linear invariance has proved fruitful in geometric function theory. One aspect of Pommerenke's work is the extension of certain results from classical univalent function theory to linearly invariant functions. We propose a definition of a related concept that we call hyperbolic linear invariance for locally schlicht holomorphic functions that map the unit disk into itself. We obtain results for hyperbolic linearly invariant functions which generalize parts of the theory of bounded univalent functions. There are many similarities between linearly invariant functions and hyperbolic linearly invariant functions, but some new phenomena also arise in the study of hyperbolic linearly invariant functions.

【 授权许可】

Unknown