An N-dimensional version of the Beurling-Ahlfors extension
arXiv:0904.3090 · doi:10.5186/aasfm.2011.3620
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.
9 pages. Added references, edited concluding remarks