Hyperbolic metrics, homogeneous holomorphic functionals and Zalcman's conjecture
Complex Variables
2012-08-15 v2
Abstract
We show, using the Kobayashi and Caratheodory metrics on special holomorphic disks in the universal Teichmuller space, that a wide class of holomorphic functionals on the space of univalent functions in the disk is maximized by the Koebe function or by its root transforms; their extremality is forced by hyperbolic features. As consequences, this implies the proofs of the famous Zalcman and Bieberbach conjectures.
Cite
@article{arxiv.1109.4646,
title = {Hyperbolic metrics, homogeneous holomorphic functionals and Zalcman's conjecture},
author = {Samuel L. Krushkal},
journal= {arXiv preprint arXiv:1109.4646},
year = {2012}
}
Comments
This is a revised and improved version of arXiv:0907.3623. Comments are welcome