Quasisymmetry and rectifiability of quasispheres
Classical Analysis and ODEs
2014-03-13 v3 Complex Variables
Metric Geometry
Abstract
We obtain Dini conditions with "exponent 2" that guarantee that an asymptotically conformal quasisphere is rectifiable. In particular, we show that for any e>0 integrability of (esssup_{1-t < |x| < 1+t} K_f(x)-1)^{2-e} dt/t implies that the image of the unit sphere under a global quasiconformal homeomorphism f is rectifiable. We also establish estimates for the weak quasisymmetry constant of a global K-quasiconformal map in neighborhoods with maximal dilatation close to 1.
Keywords
Cite
@article{arxiv.1201.1581,
title = {Quasisymmetry and rectifiability of quasispheres},
author = {Matthew Badger and James T. Gill and Steffen Rohde and Tatiana Toro},
journal= {arXiv preprint arXiv:1201.1581},
year = {2014}
}
Comments
19 pages, 3 figures (version 3: minor changes and typos fixed)