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arXiv · 1201.1581

Quasisymmetry and rectifiability of quasispheres

Matthew Badger·James T. Gill·Steffen Rohde·Tatiana Toro
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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.

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Matthew Badger, James T. Gill, Steffen Rohde, Tatiana Toro. 2012-07-31. Quasisymmetry and rectifiability of quasispheres. https://doi.org/10.1090/s0002-9947-2013-05926-0

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