摘要
This paper is devoted to the study of some fundamental properties of the sewing home- omorphism induced by a Jordan domain. In particular, using conformal invariants such as harmonic measure, extremal distance, and reduced extremal distance, we give several necessary and sumcient conditions for the sewing homeomorphism to be bi-Lipschitz or bi-Holder. Furthermore, equivalent conditions for a Jordan curve to be a quasicircle are also obtained.
This paper is devoted to the study of some fundamental properties of the sewing home- omorphism induced by a Jordan domain. In particular, using conformal invariants such as harmonic measure, extremal distance, and reduced extremal distance, we give several necessary and sumcient conditions for the sewing homeomorphism to be bi-Lipschitz or bi-Holder. Furthermore, equivalent conditions for a Jordan curve to be a quasicircle are also obtained.
基金
The first author is partially supported by National Natural Science Foundation of China(Grant Nos.11371268and 11471117)
Science and Technology Commission of Shanghai Municipality(Grant No.13dz2260400)
the third author is partially supported by National Natural Science Foundation of China(Grant No.11471117)
by PERS of Emory
