On a Hölder constant in the theory of quasiconformal mappings

Abstract

A K-quasiconformal selfmap of the unit disk with identity boundary values satisfies the Hölder estimate $|f(z)-f(w)|\le 4^{1-1/K}|z-w{|}^{1/K}$. The constant $4^{1-\frac{1}{K}}$ is sharp.

arXiv comment3 pages, typos corrected, to appear in F.W. Gehring memorial volume in CMFT