摘要
The properties of the extremal sets of extremal quasiconformal mappings are discussed. It is proved that if an extremal Beltrami coefficientμ(z) is not uniquely extremal, then there exists an extremal Beltrami coefficient v(z) in its equivalent class and a compact subset E ( ) △ with positive measure such that the essential upper bound of ν(z) on E is less than the norm of [μ].
The properties of the extremal sets of extremal quasiconformal mappings are discussed. It is proved that if an extremal Beltrami coefficient μ(z) is not uniquely extremal, then there exists an extremal Beltrami coefficient ?(z) in its equivalent class and a compact subset E ? △ with positive measure such that the essential upper bound of ?(z) on E is less than the norm of [μ].
基金
This work was supported by the National Natural Science Foundation of China(Grant No,10271029).
