Let f1 and f2 be two linearly independent solutions of the differential equation f" + Af =0,where A is an entire function.Set E-f1f2.In this paper,we shall study the angular distribution of E and establish a rela...Let f1 and f2 be two linearly independent solutions of the differential equation f" + Af =0,where A is an entire function.Set E-f1f2.In this paper,we shall study the angular distribution of E and establish a relation between zero accumulation rays and Borel directions of E.Consequently we can obtain some results in the complex differential equation by using known results in angular distribution theory of meromorphic functions.展开更多
We show that the Hausdorff dimension of quasi-circles of polygonal mappings is one.Furthermore,we apply this result to the theory of extremal quasiconformal mappings.Let [μ] be a point in the universal Teichmller spa...We show that the Hausdorff dimension of quasi-circles of polygonal mappings is one.Furthermore,we apply this result to the theory of extremal quasiconformal mappings.Let [μ] be a point in the universal Teichmller space such that the Hausdorff dimension of fμ(Δ) is bigger than one.We show that for every kn∈(0,1) and polygonal differentials ψn,n=1,2,...,the sequence {[kn ψn/|ψn|]} cannot converge to [μ] under the Teichmer metric.展开更多
We consider a symbolic coding of bi-infinite non periodic geodesics on the L-shaped translation surface tiled by three squares. Each bi-infinite non periodic geodesic is associated with a cutting sequence correspondin...We consider a symbolic coding of bi-infinite non periodic geodesics on the L-shaped translation surface tiled by three squares. Each bi-infinite non periodic geodesic is associated with a cutting sequence corresponding to the sequence of labeled saddle connections hit. We prove that there is a relationship between the cutting sequences and the actions of some affine automorphisms of the translation surface. We also get an explicit formula to determine the direction of a bi-infinite non periodic geodesic by using the corresponding cutting sequence.展开更多
For any multiply connected domain Ω in R2, let S be the boundary of the convex hull in H3 of R2\Ω which faces Ω. Suppose in addition that there exists a lower bound l > 0 of the hyperbolic lengths of closed geod...For any multiply connected domain Ω in R2, let S be the boundary of the convex hull in H3 of R2\Ω which faces Ω. Suppose in addition that there exists a lower bound l > 0 of the hyperbolic lengths of closed geodesics in Ω. Then there is always a K-quasiconformal mapping from S to Ω, which extends continuously to the identity on S = Ω, where K depends only on l. We also give a numerical estimate of K by using the parameter l.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.10171003 and 10231040)the Doctoral Education Program Foundation of China.
文摘Let f1 and f2 be two linearly independent solutions of the differential equation f" + Af =0,where A is an entire function.Set E-f1f2.In this paper,we shall study the angular distribution of E and establish a relation between zero accumulation rays and Borel directions of E.Consequently we can obtain some results in the complex differential equation by using known results in angular distribution theory of meromorphic functions.
基金supported by National Natural Science Foundation of China(Grant Nos.10831004 and 11171080)
文摘We show that the Hausdorff dimension of quasi-circles of polygonal mappings is one.Furthermore,we apply this result to the theory of extremal quasiconformal mappings.Let [μ] be a point in the universal Teichmller space such that the Hausdorff dimension of fμ(Δ) is bigger than one.We show that for every kn∈(0,1) and polygonal differentials ψn,n=1,2,...,the sequence {[kn ψn/|ψn|]} cannot converge to [μ] under the Teichmer metric.
基金supported by National Natural Science Foundation of China(Grant No.11371035)
文摘We consider a symbolic coding of bi-infinite non periodic geodesics on the L-shaped translation surface tiled by three squares. Each bi-infinite non periodic geodesic is associated with a cutting sequence corresponding to the sequence of labeled saddle connections hit. We prove that there is a relationship between the cutting sequences and the actions of some affine automorphisms of the translation surface. We also get an explicit formula to determine the direction of a bi-infinite non periodic geodesic by using the corresponding cutting sequence.
基金supported by National Natural Science Foundation of China (Grant Nos. 10671004, 10831004)the Doctoral Education Program Foundation of China (Grant No. 20060001003)
文摘For any multiply connected domain Ω in R2, let S be the boundary of the convex hull in H3 of R2\Ω which faces Ω. Suppose in addition that there exists a lower bound l > 0 of the hyperbolic lengths of closed geodesics in Ω. Then there is always a K-quasiconformal mapping from S to Ω, which extends continuously to the identity on S = Ω, where K depends only on l. We also give a numerical estimate of K by using the parameter l.
基金supported by National Natural Science Foundation of China (Grant Nos.10671004,10831004)The Doctoral Education Program Foundation (Grant No.20060001003)
文摘We show that the extremal polygonal quasiconformal mappings are biLipschitz with respect to the hyperbolic metric in the unit disk.
