Boundary distortion estimates for holomorphic maps
Complex Variables
2013-09-13 v1
Abstract
We establish some estimates of the the angular derivatives from below for holomorphic self-maps of the unit disk at one and two fixed points of the unit circle provided there is no fixed point inside the unit disk. The results complement Cowen-Pommerenke and Anderson-Vasil'ev type estimates in the case of univalent functions. We use the method of extremal length and propose a new semigroup approach to deriving inequalities for holomorphic self-maps of the disk which are not necessarily univalent using known inequalities for univalent functions. This approach allowed us to receive a new Ossermans type estimate as well as inequalities for holomorphic self-maps which images do not separate the origin and the boundary.
Cite
@article{arxiv.1309.3074,
title = {Boundary distortion estimates for holomorphic maps},
author = {A. Frolova and M. Levenshtein and D. Shoikhet and A. Vasil'ev},
journal= {arXiv preprint arXiv:1309.3074},
year = {2013}
}