Extremal quasiconformality vs rational approximation
arXiv:1912.08980 · doi:10.1007/s10958-019-04601-6
Abstract
We show that on most of the hyperbolic simply connected domains the weighted bounded rational approximation in a natural sup norm is possible only for a very sparse set of holomorphic functions (in contrast to integral approximation). The obstructions are caused by the features of extremal quasiconformality.