In this paper, we consider and resolve a geometric problem by using μ（z）-homeomorphic theory, which is the generalization of quasiconformal mappings. A sufficient condition is given such that a Ct-two-real-dimensio...In this paper, we consider and resolve a geometric problem by using μ（z）-homeomorphic theory, which is the generalization of quasiconformal mappings. A sufficient condition is given such that a Ct-two-real-dimensional connected orientable manifold with almost positive definite metric can be made into a Riemann surface by the method of isothermal coordinates. The result obtained here is actually a generalization of Chern＇s work in 1955.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
In this paper,a distortion theorem and some equicontinuity and compactness theorems are obtained for the homeomorphism f with the sphere dilatation H（x,f）∈L<sub>loc</sub>（D）.
基金Project (No. 10101023) supported by the National Natural Science Foundation of China
文摘In this paper, we consider and resolve a geometric problem by using μ（z）-homeomorphic theory, which is the generalization of quasiconformal mappings. A sufficient condition is given such that a Ct-two-real-dimensional connected orientable manifold with almost positive definite metric can be made into a Riemann surface by the method of isothermal coordinates. The result obtained here is actually a generalization of Chern＇s work in 1955.
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Supported by the National Natural Science Foundation of China the Dctoral Foundation of the Education Commission of China
文摘In this paper,a distortion theorem and some equicontinuity and compactness theorems are obtained for the homeomorphism f with the sphere dilatation H（x,f）∈L<sub>loc</sub>（D）.
