ABSTRACT. Zygmund bounded vector fields are defined on arbitrary closed sets in the complex plane. The infinitesimal Teichmuller norm and the cross-ratio norm are shown to be equivalent. Vector fields representable by vanishing Beltrami differentials are shown to coincide with vector fields which satisfy a vanishing cross-ratio property.
The paper is a part of LIPA's LEGACY , Contemporary Mathematics, Vol. 211, AMS.
This volume is based on the Proceedings of the Bers Colloquium, held in New York City in October 1995.