Univalent functions and Diff(S 1)/S 1

Abstract

The relation between Diff(S 1 )/S 1 and the space of univalent analytic functions on the disk is elucidated and shown to provide upper bounds for the volumes of exhaustive approximations to an analytic submanifold of an infinite-dimensional space. The maximum magnitudes of the coefficients in the series expansions of univalent superanalytic functions on the superdisk are inferred.