拟共形映射与Turning域

Quasi-conformal Mappings and Turning Domains

讨论了拟共形映射与Turning域及ILC域之间的关系.首先根据拟共形映射与Turning域的性质得到f是拟共形映射的充要条件是f将Rn中的Turning域映成Rn中的Turning域;然后根据Turning域及ILC域的等价性得到f是拟共形映射的充要条件是f将Rn中的ILC域映成Rn中的ILC域.

The relation of quasi-conformal mappings and Turning domains,ILC domains are discussed.Firstly,on the basis of properties of quasi-conformal mappings and Turning domains,we obtain that f is a quasi-conformal mapping if and only if the Turning domains in Rn are invariant under f;and then by equivalence of Turning domains and ILC domains we conolude that f is a quasi-conformal mapping if and only if the ILC domains in Rn are invariant under f.