Toshiyuki SUGAWA
Holomorphic motions and quasiconformal extensions
Abstract
In this article, we will consider holomorphic families of univalent functions
parametrized by the unit disk in such a way that the origin corresponds to
the identity.
For each member of the family, thanks to the $\lambda$-lemma, we then have a
quasiconformal extension of it.
This method enables us not only to give simple proofs of some known results,
but also to provide new results.
We will discuss about quasiconformal extendability of some tipical classes
of univalent functions by the above method.
submission: August 1, 1998
revision: August 7, 1998
revision: November 19, 1998
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