Toshiyuki SUGAWA

Holomorphic motions and quasiconformal extensions


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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