双曲区域上拟共形映照的极值问题(英文)

An Extremal Problem of Quasiconformal Mappings in Hyperbolic Regions

证明了对于双曲区域 {z =x +iy :x2a2 - y2b2 >1,x >0 }上的仿射拉伸AK(z) =Kx +iy的边界对应 ,其极值最大伸缩商等于区域上任意拓扑四边形的共形模与其像所构成的拓扑四边形的共形模之比的上确界 .

The boundary correspondence of the affine stretch A K(z)=K x+iy in the hyperbolic regions{z=x+iy:x 2a 2-y 2b 2>1,x>0} is proved to have the property that the extremal maximal dilatation is equal to the supremum of the ratios of the moduli of quadrilaterals.