The rectifiability of certain quasicircles

Abstract

Suppose that the quasiconformal homeomorphism fof the complex plane fixes the point at infinity, is conformal in the exterior of the unit disk, and that the complex dilatation μ of f satisfies

for some positive δ. It is shown that then fmaps the unit circle onto a rectifiable quasicircle.

AMS(MOS)::

• 30C60

^*Research partially supported by the U.S. National Science Foundation

^*Research partially supported by the U.S. National Science Foundation

Notes

^*Research partially supported by the U.S. National Science Foundation