Chordal Loewner Equation
Abstract
The aim of this survey paper is to present a complete direct proof of the well celebrated cornerstone result in Loewner Theory, originally due to Kufarev et al [Trudy Tomsk. Gos. Univ. Ser. Meh.-Mat. 200 (1968) 142-164. MR0257336 (41 #1987)], stating that the family of the hydrodynamically normalized conformal self-maps of the upper-half plane onto the complement of a gradually erased slit satisfies, under a suitable parametrization, the chordal Loewner differential equation. The proof is based solely on basic theorems of Geometric Function Theory combined with some elementary topological facts and does not require any advanced technique.
Keywords
Cite
@article{arxiv.1302.0898,
title = {Chordal Loewner Equation},
author = {Andrea del Monaco and Pavel Gumenyuk},
journal= {arXiv preprint arXiv:1302.0898},
year = {2013}
}
Comments
A minor mistake in the proof of Proposition 2.2 is corrected, thanks to Iason Efraimidis (Universidad Autonoma de Madrid)