Conformality of quasiconformal mappings at a point, revisited

Published 26 Feb 2018 in math.CV | (1802.09137v2)

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 $C^{{1+\alpha}$-conformality}