Asymptotic Conformality of the Barycentric Extension of Quasiconformal Maps

作者：Matsuzaki Katsuhiko^*; Yanagishita Masahiro

来源：Filomat, 2017, 31(1): 85-90.

DOI：10.2298/FIL1701085M

• integrable Teichmuller space
• barycentric extension
• complex dilatation
• quasiconformal
• asymptotically conformal
• Teichmuller projection
• Bers embedding

We first remark that the complex dilatation of a quasiconformal homeomorphism of a hyperbolic Riemann surface R obtained by the barycentric extension due to Douady-Earle vanishes at any cusp of R. Then we give a new proof, without using the Bers embedding, of a fact that the quasiconformal homeomorphism obtained by the barycentric extension from an integrable Beltrami coe ffi cient on R is asymptotically conformal if R satisfies a certain geometric condition.

• 出版日期2017