TY - JOUR
T1 - Asymptotic conformality of the Barycentric extension of quasiconformal maps
AU - Matsuzaki, Katsuhiko
AU - Yanagishita, Masahiro
N1 - Funding Information:
Research supported by JSPS Grant-in-Aid for Scientific Research (B) 25287021a and Grant-in-Aid for JSPS Fellows 14J03444b
Publisher Copyright:
© 2017, University of Nis. All rights reserved.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017
Y1 - 2017
N2 - 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 coefficient on R is asymptotically conformal if R satisfies a certain geometric condition.
AB - 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 coefficient on R is asymptotically conformal if R satisfies a certain geometric condition.
KW - Asymptotically conformal
KW - Barycentric extension
KW - Bers embedding
KW - Complex dilatation
KW - Integrable teichmüller space
KW - Quasiconformal
KW - Teichmüller projection
UR - http://www.scopus.com/inward/record.url?scp=85012284341&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85012284341&partnerID=8YFLogxK
U2 - 10.2298/FIL1701085M
DO - 10.2298/FIL1701085M
M3 - Article
AN - SCOPUS:85012284341
SN - 0354-5180
VL - 31
SP - 85
EP - 90
JO - Filomat
JF - Filomat
IS - 1
ER -