Conformality of quasiconformal mappings at a point, revisited
Complex Variables
2018-05-01 v2
Abstract
We present a new and simple proof of Teichm\"uller-Wittich-Belinskii's and Gutlyanskii-Martio's theorems on the conformality of quasiconformal mappings at a given point. Known proofs gave separate estimates for the radial and angular variations, but our proof unifies them using Gr\"otzsch-type inequality for the variation of cross-ratio of four points on the Riemann sphere. We also give a sufficient condition for -conformality
Keywords
Cite
@article{arxiv.1802.09137,
title = {Conformality of quasiconformal mappings at a point, revisited},
author = {Mitsuhiro Shishikura},
journal= {arXiv preprint arXiv:1802.09137},
year = {2018}
}