In this paper,the following two results are obtained:(1) If Γ is a Jordan curve of 2,∞∈Γ,then Γ is a quasicircle if and only if there exists a constant k,1≤k<+∞,such that for any four points z 1,z 2,w 1,w...In this paper,the following two results are obtained:(1) If Γ is a Jordan curve of 2,∞∈Γ,then Γ is a quasicircle if and only if there exists a constant k,1≤k<+∞,such that for any four points z 1,z 2,w 1,w 2∈Γ,there exists a k-quasiconformal mapping h of 2 with h(∞)=∞,h(Γ)=Γ and h(z j)=w j(j=1,2).(2)If Γ is a Jordan curve of 2, then Γ is a quasicircle if and only if Γ is a bounded circular distortion curve.展开更多
A generalized Beurling-Ahlfors’ Theorem for the self homeomorphism f of the upper half plane with the sphere dilatation H(z,f) L (H) is established and the property of weighted quasi-isometry for the generalized Beur...A generalized Beurling-Ahlfors’ Theorem for the self homeomorphism f of the upper half plane with the sphere dilatation H(z,f) L (H) is established and the property of weighted quasi-isometry for the generalized Beurling-Ahlfors’ extension is studied.展开更多
This paper is devoted to the study of some fundamental properties of the sewing home- omorphism induced by a Jordan domain. In particular, using conformal invariants such as harmonic measure, extremal distance, and re...This paper is devoted to the study of some fundamental properties of the sewing home- omorphism induced by a Jordan domain. In particular, using conformal invariants such as harmonic measure, extremal distance, and reduced extremal distance, we give several necessary and sumcient conditions for the sewing homeomorphism to be bi-Lipschitz or bi-Holder. Furthermore, equivalent conditions for a Jordan curve to be a quasicircle are also obtained.展开更多
Let U be an open subset of the Riemann sphere C. We give sufficient conditions for which a finite type map f : U →C with at most three singular values has a Siegel disk compactly contained in U and whose boundary is ...Let U be an open subset of the Riemann sphere C. We give sufficient conditions for which a finite type map f : U →C with at most three singular values has a Siegel disk compactly contained in U and whose boundary is a quasicircle containing a unique critical point. The main tool is quasiconformal surgery à la Douady-Ghys-Herman-(S′)wia tek. We also give sufficient conditions for which, instead, ? has not compact closure in U. The main tool is the Schwarzian derivative and area inequalities à la Graczyk-(S′)wia tek.展开更多
We prove that for any bounded type irrational number 0 〈 0 〈 1, the boundary of theSiegel disk of fα（z） = e^2πiθsin（z） ＋ αsin^3（z）, a E C, which centered at the origin, is a quasicircle passing through 2,...We prove that for any bounded type irrational number 0 〈 0 〈 1, the boundary of theSiegel disk of fα（z） = e^2πiθsin（z） ＋ αsin^3（z）, a E C, which centered at the origin, is a quasicircle passing through 2, 4 or 6 critical points of fα counted with multiplicity.展开更多
基金Supported by the National Natural Science Foundation of China( 1 0 2 71 0 4 3) and the Natural ScienceFoundation of Zhejiang province ( M1 0 30 87)
文摘In this paper,the following two results are obtained:(1) If Γ is a Jordan curve of 2,∞∈Γ,then Γ is a quasicircle if and only if there exists a constant k,1≤k<+∞,such that for any four points z 1,z 2,w 1,w 2∈Γ,there exists a k-quasiconformal mapping h of 2 with h(∞)=∞,h(Γ)=Γ and h(z j)=w j(j=1,2).(2)If Γ is a Jordan curve of 2, then Γ is a quasicircle if and only if Γ is a bounded circular distortion curve.
基金the National Natural Science Foundation of China (Tian Yuan) and Shanghai Jiaotong University
文摘A generalized Beurling-Ahlfors’ Theorem for the self homeomorphism f of the upper half plane with the sphere dilatation H(z,f) L (H) is established and the property of weighted quasi-isometry for the generalized Beurling-Ahlfors’ extension is studied.
基金The first author is partially supported by National Natural Science Foundation of China(Grant Nos.11371268and 11471117)Science and Technology Commission of Shanghai Municipality(Grant No.13dz2260400)+1 种基金the third author is partially supported by National Natural Science Foundation of China(Grant No.11471117)by PERS of Emory
文摘This paper is devoted to the study of some fundamental properties of the sewing home- omorphism induced by a Jordan domain. In particular, using conformal invariants such as harmonic measure, extremal distance, and reduced extremal distance, we give several necessary and sumcient conditions for the sewing homeomorphism to be bi-Lipschitz or bi-Holder. Furthermore, equivalent conditions for a Jordan curve to be a quasicircle are also obtained.
文摘Let U be an open subset of the Riemann sphere C. We give sufficient conditions for which a finite type map f : U →C with at most three singular values has a Siegel disk compactly contained in U and whose boundary is a quasicircle containing a unique critical point. The main tool is quasiconformal surgery à la Douady-Ghys-Herman-(S′)wia tek. We also give sufficient conditions for which, instead, ? has not compact closure in U. The main tool is the Schwarzian derivative and area inequalities à la Graczyk-(S′)wia tek.
基金Supported by National Natural Science Foundation of China(Grant No.11231009)
文摘We prove that for any bounded type irrational number 0 〈 0 〈 1, the boundary of theSiegel disk of fα（z） = e^2πiθsin（z） ＋ αsin^3（z）, a E C, which centered at the origin, is a quasicircle passing through 2, 4 or 6 critical points of fα counted with multiplicity.
基金Project supported by the National Natural Science Foundation of China.
文摘We make improvements to some of the constants concerned with univalent functions with quasiconformal extensions that have appeared in the literature.
