Singular solutions to the Loewner equation
Complex Variables
2008-09-29 v2
Abstract
We consider the L\"owner differential equation generating univalent self-maps of the unit disk (or of the upper half-plane). If the solution to this equation represents a one-slit map, then the driving term is a continuous function. The reverse statement is not true in general as a famous Kufarev's example shows. We address the following main problem: to find a criterium for the L\"owner equation to generate one-slit solutions. New examples of non-slit solutions to the L\"owner equation are presented. Properties of singular slit solutions are revealed.
Cite
@article{arxiv.0807.0519,
title = {Singular solutions to the Loewner equation},
author = {Dmitri Prokhorov and Alexander Vasil'ev},
journal= {arXiv preprint arXiv:0807.0519},
year = {2008}
}
Comments
14 pages, figures are added