By applying the theory of quasiconformal maps in measure metric spaces that was introduced by Heinonen-Koskela, we characterize bi-Lipschitz maps by modulus inequalities of rings and maximal, minimal derivatives in Q-...By applying the theory of quasiconformal maps in measure metric spaces that was introduced by Heinonen-Koskela, we characterize bi-Lipschitz maps by modulus inequalities of rings and maximal, minimal derivatives in Q-regular Loewner spaces. Meanwhile the sufficient and necessary conditions for quasiconformal maps to become bi-Lipschitz maps are also obtained. These results generalize Rohde’s theorem in ? n and improve Balogh’s corresponding results in Carnot groups.展开更多
The purpose of this paper is to give a relatively elementary and direct proof of the Delta Inequality, which plays a very important role in the study of the extremal problem of quasiconformal mappings.
In this paper,a new version of the general form of the main inequality of Reich-Strebel is given.As applications,we improve the strong triangle inequality and generalize the Delta inequality in certain sense.
文摘By applying the theory of quasiconformal maps in measure metric spaces that was introduced by Heinonen-Koskela, we characterize bi-Lipschitz maps by modulus inequalities of rings and maximal, minimal derivatives in Q-regular Loewner spaces. Meanwhile the sufficient and necessary conditions for quasiconformal maps to become bi-Lipschitz maps are also obtained. These results generalize Rohde’s theorem in ? n and improve Balogh’s corresponding results in Carnot groups.
基金supported by the National Natural Science Foundation of China(10971008 and 11371045)
文摘The purpose of this paper is to give a relatively elementary and direct proof of the Delta Inequality, which plays a very important role in the study of the extremal problem of quasiconformal mappings.
基金supported by National Natural Science Foundation of China(Grant No.10971008)
文摘In this paper,a new version of the general form of the main inequality of Reich-Strebel is given.As applications,we improve the strong triangle inequality and generalize the Delta inequality in certain sense.
