Finding complete conformal metrics to extend conformal mappings
M. ChuaquiB. Osgood
30C3530C62
This paper shows how new differential geometric approaches to univalence criteria involving the Schwarzian derivative can be applied to a classical, but very general, criterion of Nehari. We show how positive solutions to the second order ODE associated to the Schwarzian can be used to construct complete conformal metrics. These lead to explicit formulas for homeomorphic and quasiconformal extensions of conformal mappings as generalizations of the Ahlfors-Weill extension.
Indiana University Mathematics Journal
1998
text
pdf
10.1512/iumj.1998.47.1606
10.1512/iumj.1998.47.1606
en
Indiana Univ. Math. J. 47 (1998) 1273 - 1292
state-of-the-art mathematics
http://iumj.org/access/