The distortion property of hyperbolic area of planar quasiconformal mappings is studied in this paper. In the case of radial quasiconformal mappings and angular deformed quasiconformal mappings their hyperbolic area d...The distortion property of hyperbolic area of planar quasiconformal mappings is studied in this paper. In the case of radial quasiconformal mappings and angular deformed quasiconformal mappings their hyperbolic area distortions are estimated quite sharply. The result can be applied to judge whether the hyperbolic area of a planar subset is explodable.展开更多
In this article,we first give two simple examples to illustrate that two types of parametric representation of the family ofΣ0 K have some gaps.Then we also find that the area derivative formula(1.6),which is used to...In this article,we first give two simple examples to illustrate that two types of parametric representation of the family ofΣ0 K have some gaps.Then we also find that the area derivative formula(1.6),which is used to estimate the area distortion ofΣ0 K,cannot be derived from[6],but that formula still holds forΣ0 K through our amendatory parametric representation for the one obtained by Eremenko and Hamilton.展开更多
考虑如下极值问题:inf f∈ΛQ 1αf x^(2)+βf y^(2)J(z,f)/d x d y,α>0,β>0,其中Λ是矩形Q_(1)=[0,l]×[0,1]到矩形Q_(2)=[0,L]×[0,1]并保持端点对应的有限偏差的集合。同时借助经典的面积长度方法和平均值不等式方...考虑如下极值问题:inf f∈ΛQ 1αf x^(2)+βf y^(2)J(z,f)/d x d y,α>0,β>0,其中Λ是矩形Q_(1)=[0,l]×[0,1]到矩形Q_(2)=[0,L]×[0,1]并保持端点对应的有限偏差的集合。同时借助经典的面积长度方法和平均值不等式方法分别证明了仿射拉伸变换为该极值问题的解。该结果推广了Astala等的结果。展开更多
基金Supported by the Natural Science Foundation of Huaqiao University(02HZR12)Supported by the Natural Science Foundation of Overseas Chinese Affairs Office under the State Council(01QZR01)
文摘The distortion property of hyperbolic area of planar quasiconformal mappings is studied in this paper. In the case of radial quasiconformal mappings and angular deformed quasiconformal mappings their hyperbolic area distortions are estimated quite sharply. The result can be applied to judge whether the hyperbolic area of a planar subset is explodable.
基金National Natural Science Foundation of China(11971182)the Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University(ZQN-PY402)+1 种基金Research projects of Young and Middle-aged Teacher's Education of Fujian Province(JAT190508)Scientific research project of Quanzhou Normal University(H19009).
文摘In this article,we first give two simple examples to illustrate that two types of parametric representation of the family ofΣ0 K have some gaps.Then we also find that the area derivative formula(1.6),which is used to estimate the area distortion ofΣ0 K,cannot be derived from[6],but that formula still holds forΣ0 K through our amendatory parametric representation for the one obtained by Eremenko and Hamilton.
文摘考虑如下极值问题:inf f∈ΛQ 1αf x^(2)+βf y^(2)J(z,f)/d x d y,α>0,β>0,其中Λ是矩形Q_(1)=[0,l]×[0,1]到矩形Q_(2)=[0,L]×[0,1]并保持端点对应的有限偏差的集合。同时借助经典的面积长度方法和平均值不等式方法分别证明了仿射拉伸变换为该极值问题的解。该结果推广了Astala等的结果。
