TY - JOUR
T1 - Criteria for univalence and quasiconformal extension of harmonic mappings in terms of the Schwarzian derivative
AU - Hernández, Rodrigo
AU - Martín, María J.
N1 - Publisher Copyright:
© 2014, Springer Basel.
PY - 2014/1
Y1 - 2014/1
N2 - We prove that if the Schwarzian norm of a given complex-valued locally univalent harmonic mapping f in the unit disk is small enough, then f is, indeed, globally univalent in the unit disk and can be extended to a quasiconformal mapping in the extended complex plane.
AB - We prove that if the Schwarzian norm of a given complex-valued locally univalent harmonic mapping f in the unit disk is small enough, then f is, indeed, globally univalent in the unit disk and can be extended to a quasiconformal mapping in the extended complex plane.
KW - Harmonic mapping
KW - Quasiconformal extension
KW - Schwarzian derivative
KW - Univalence criterion
UR - http://www.scopus.com/inward/record.url?scp=84925482269&partnerID=8YFLogxK
U2 - 10.1007/s00013-014-0714-5
DO - 10.1007/s00013-014-0714-5
M3 - Article
AN - SCOPUS:84925482269
SN - 0003-889X
VL - 104
SP - 53
EP - 59
JO - Archiv der Mathematik
JF - Archiv der Mathematik
IS - 1
ER -