1Shantou University, Department of Mathematics 2Hunan Normal University, School of Mathematics and Statistics, MOE-LCSM, and Qufu Normal University, School of Mathematical Science 3Hunan Normal University, School of Mathematics and Statistics, MOE-LCSM
Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 771-779
Cet article a éte moissonné depuis la source Journal.fi
Suppose that $G\subsetneq E$ and $G'\subsetneq E'$ are domains, where $E$ and $E'$ denote real Banach spaces with dimension at least 2, and $f\colon G\to G'$ is a homeomorphism. The aim of this paper is to prove the validity of the implications: $f$ is $M$-bilipschitz $\Rightarrow f$ is locally $M$-bilipschitz $\Rightarrow f$ is $M$-QH $\Rightarrow f$ is locally $M$-QH, and the invalidity of their opposite implications, i.e., $f$ is locally $M$-QH $\nRightarrow f$ is $M$-QH $\nRightarrow f$ is locally $M$-bilipschitz $\nRightarrow f$ is $M$-bilipschitz. Among these results, the relationship that $f$ is locally $M$-QH $\nRightarrow f$ is $M$-QH gives a negative answer to one of the open problems raised by Väisälä in 1999.
1
Shantou University, Department of Mathematics
2
Hunan Normal University, School of Mathematics and Statistics, MOE-LCSM, and Qufu Normal University, School of Mathematical Science
3
Hunan Normal University, School of Mathematics and Statistics, MOE-LCSM
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author = {Yuehui He and Manzi Huang and Xiantao Wang},
title = {Bilipschitz mappings and quasihyperbolic mappings in real {Banach} spaces},
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year = {2021},
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Yuehui He; Manzi Huang; Xiantao Wang. Bilipschitz mappings and quasihyperbolic mappings in real Banach spaces. Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 771-779. http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a11/
