Singular and tangent slit solutions to the Loewner equation
Complex Variables
2008-06-23 v2
Abstract
We consider the Loewner differential equation generating univalent maps of the unit disk (or of the upper half-plane) onto itself minus a single slit. We prove that the circular slits, tangent to the real axis are generated by H\"older continuous driving terms with exponent 1/3 in the Loewner equation. Singular solutions are described, and the critical value of the norm of driving terms generating quasisymmetric slits in the disk is obtained.
Keywords
Cite
@article{arxiv.0708.1048,
title = {Singular and tangent slit solutions to the Loewner equation},
author = {Dmitri Prokhorov and Alexander Vasil'ev},
journal= {arXiv preprint arXiv:0708.1048},
year = {2008}
}
Comments
8 pages