Exponential driving function for the L\"owner equation
Complex Variables
2012-01-05 v1
Abstract
We consider the chordal L\"owner differential equation with the model driving function . Holomorphic and singular solutions are represented by their series. It is shown that a disposition of values of different singular and branching solutions is monotonic, and solutions to the L\"owner equation map slit domains onto the upper half-plane. The slit is a -curve. We give an asymptotic estimate for the ratio of harmonic measures of the two slit sides.
Cite
@article{arxiv.1201.0886,
title = {Exponential driving function for the L\"owner equation},
author = {Dmitri Prokhorov},
journal= {arXiv preprint arXiv:1201.0886},
year = {2012}
}