John Disk And Quasiconformal Mapping,Quasihyperbolic Metric

This thesis is concerned with some properties of John disk,K-quasiconformal har-monic mapping and quasi-hyperbolic.We draw two inferences and an equivalent condition and a necessary condition for John disk.This paper composed of three chapters.In chapter one,we briefly introduce the related knowledge and developmental back-ground of John disk.Then we will know the research foundation of this paper and the significance of the results.In chapter two,we mainly discuss the properties of John disk under the K-quasiconform-al harmonic mapping f,and obtain an equivalent condition of the John disk,which makes the relationship between the John circle and the quasiconformal harmonic mapping more closely.In chapter three,we mainly discuss the correlation between John disk and quasi-hyperbolic metrics,and obtain a necessary condition for John disk,which makes us have a further understanding of the relationship between John disk and quasi-hyperbolic metrics.The main result of this thesis is the breadth and the deep into further study under some know results,we improve and generalize some former researches.Through the work of this paper,the relationship between John disk and the quasiconformal mapping and the quasi-hyperbolic metrics is further enhanced.