In this paper, we provefunction of Beurling-Ahlfors extensionthat the control function of the dilatation is convex. Using the quasi-symmetric function p, we get a relatively sharp estimate of the dilatation function: ...In this paper, we provefunction of Beurling-Ahlfors extensionthat the control function of the dilatation is convex. Using the quasi-symmetric function p, we get a relatively sharp estimate of the dilatation function: D(x,y) < 17/32 (p(x, y) + 1) (p(x + y/2, y/2) + p(x-y/2, y/2) + 2) , which improves the results before.We also show that the above result is asymptotically precise.展开更多
In this paper, we study the Beurling-Ahlfors extensions and prove two results. The first variation of the Beurling-Ahlfors extension is not always harmonic; the Beurling-Ahlfors extension of a quasisymmetric mapping i...In this paper, we study the Beurling-Ahlfors extensions and prove two results. The first variation of the Beurling-Ahlfors extension is not always harmonic; the Beurling-Ahlfors extension of a quasisymmetric mapping is not always harmonic.展开更多
The Beurling-Ahlfors’ extension is studied under relatively general conditions and its dilatation fonction is estimated. Particularly, the classic Deurling -Ahlfors’ theorem can be obtained under the M-condition.
设h(x)是实轴上的保向同胚,满足h(±∞)=±∞.当h(x)的拟对称函数(,)()()()()x th x t h xρ=h x+?h?x?t(x∈R,t>0)被递减函数ρ(t)所控制时,h(x)的Beurling-Ahlfors扩张的伸缩商D(z)具有下述估计:21 1D≤ρ?+ρ??2,其中()2...设h(x)是实轴上的保向同胚,满足h(±∞)=±∞.当h(x)的拟对称函数(,)()()()()x th x t h xρ=h x+?h?x?t(x∈R,t>0)被递减函数ρ(t)所控制时,h(x)的Beurling-Ahlfors扩张的伸缩商D(z)具有下述估计:21 1D≤ρ?+ρ??2,其中()2ρ?=ρy.展开更多
基金Supported by the National Natural Science Foundation of China(10271077)Supported by the Educational Department of Zhejiang Province Natural Science Project(20030768)
文摘In this paper, we provefunction of Beurling-Ahlfors extensionthat the control function of the dilatation is convex. Using the quasi-symmetric function p, we get a relatively sharp estimate of the dilatation function: D(x,y) < 17/32 (p(x, y) + 1) (p(x + y/2, y/2) + p(x-y/2, y/2) + 2) , which improves the results before.We also show that the above result is asymptotically precise.
基金The NSF (11101290) for Young Scientists of China,the NSF (11071179,10871211) of ChinaScientific Research Starting Foundation (00035242) of Shenzhen University
文摘In this paper, we study the Beurling-Ahlfors extensions and prove two results. The first variation of the Beurling-Ahlfors extension is not always harmonic; the Beurling-Ahlfors extension of a quasisymmetric mapping is not always harmonic.
文摘The Beurling-Ahlfors’ extension is studied under relatively general conditions and its dilatation fonction is estimated. Particularly, the classic Deurling -Ahlfors’ theorem can be obtained under the M-condition.
文摘设h(x)是实轴上的保向同胚,满足h(±∞)=±∞.当h(x)的拟对称函数(,)()()()()x th x t h xρ=h x+?h?x?t(x∈R,t>0)被递减函数ρ(t)所控制时,h(x)的Beurling-Ahlfors扩张的伸缩商D(z)具有下述估计:21 1D≤ρ?+ρ??2,其中()2ρ?=ρy.
