摘要
By studying the existence problem of locally extremal Beltrami differential posed by F. Gardiner and N. Lakic, we introduce a new definition of the local boundary dilatations of points in Teichmuller spaces of simply connected plane domains, which is the same as the usual ones in the case of Jordan domains. Then we show that the answer to the problem of F. Gardiner and N. Lakic is affirmative according to this new definition. Comparing with the usual definitions, the problem of F. Gardiner and N. Lakic is partly answered and the results of G. Cui and Y. Qi is generalized.
By studying the existence problem of locally extremal Beltrami differential posed by F. Gardiner and N. Lakic, we introduce a new definition of the local boundary the same as the usual ones in the case of Jordan domains. Then we show that the answer to the problem of F. Gardiner and N. Lakic is affirmative according to this new definition. Comparing with the usual definitions, the problem of F. Gardiner and N. Lakic is partly answered and the results of G. Cui and Y. Qi is generalized.
基金
The author would like to thank Professor Cui Guizhen for helpful discussions.This work was supported by the National Natural Science Foundation of China(Grant No.10271063).
