拟共形映照的双曲面积偏差  

Hyperbolic Area Distortion under Quasiconformal Mappings

作　　者：韩雪[1] 黄心中[1] 

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《华侨大学学报（自然科学版）》2007年第4期433-436,共4页Journal of Huaqiao University(Natural Science)

基　　金：福建省自然科学基金资助项目(Z0511025)

摘　　要：进一步研究拟共形映照f(z)=ρ(r,θ)eiφ(θ),z=reiθ,0<r<1,在一定条件下双曲面积的偏差,得到拟共形映照f(z)=ρ(r,θ)eiφ(θ),z=reiθ,0<r<1,f(1)=1,满足0<δ≤φ′(θ)≤M,0<a<1,对任何可测集EΔ,若|E|hyp<∞,一定有|f(E)|hyp<∞,即f一定是非爆破的.同时,还证明如果f(z)为单位圆Δ到自身上的调和拟共形映照,则f(z)是非爆破的.Two-dimensional hyperbolic area distortion under a class of quasiconformal mappings in the unit disk is estimated . As application, the fact that any bounded hyperbolic area set under these mappings can＇t be exploded has been proved. Our results extend some previous results of CHFN Xing-di. At last a sort of nonexplodable harmonic quasiconformal mappings is obtained.

关 键 词：拟共形映照 调和拟共形映照 双曲面积 爆破集 

分 类 号：O174.55[理学—数学]