An N-dimensional version of the Beurling-Ahlfors extension
Complex Variables
2011-02-08 v2
Abstract
We extend monotone quasiconformal mappings from dimension n to n+1 while preserving both monotonicity and quasiconformality. The extension is given explicitly by an integral operator. In the case n=1 it yields a refinement of the Beurling-Ahlfors extension.
Keywords
Cite
@article{arxiv.0904.3090,
title = {An N-dimensional version of the Beurling-Ahlfors extension},
author = {Leonid V. Kovalev and Jani Onninen},
journal= {arXiv preprint arXiv:0904.3090},
year = {2011}
}
Comments
9 pages. Added references, edited concluding remarks