Euclidean and hyperbolic lenghs of images of arcs
Complex Variables
2014-02-26 v1
Abstract
Let be a function that is analytic in the unit disc. We give new estimates, and new proofs of existing estimates, of the Euclidean length of the image under of a radial segment in the unit disc. Our methods are based on the hyperbolic geometry of plane domains, and we address some new questions that follow naturally from this approach.
Keywords
Cite
@article{arxiv.0711.0219,
title = {Euclidean and hyperbolic lenghs of images of arcs},
author = {A. F. Beardon and T. K. Carne},
journal= {arXiv preprint arXiv:0711.0219},
year = {2014}
}
Comments
26 pages