Géométrie
Quasihyperbolic mappings in length metric spaces
Comptes Rendus. Mathématique, Tome 359 (2021) no. 3, pp. 237-247.

In this paper, we discuss the local properties of quasihyperbolic mappings in metric spaces, which are related to an open problem raised by Huang et al in 2016. Our result is a partial solution to this problem, which is also a generalization of the corresponding result obtained by Huang et al in 2016.

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DOI : 10.5802/crmath.154
Classification : 30L10, 53C23, 30L99, 30F10
Zhou, Qingshan 1 ; Li, Yaxiang 2 ; He, Yuehui 3

1 School of Mathematics and Big Data, Foshan university, Foshan, Guangdong 528000, People’s Republic of China
2 Department of Mathematics, Hunan First Normal University, Changsha, Hunan 410205, People’s Republic of China
3 Department of Mathematics, Shantou University, Shantou, Guangdong 515063, People’s Republic of China
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     title = {Quasihyperbolic mappings in length metric spaces},
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Zhou, Qingshan; Li, Yaxiang; He, Yuehui. Quasihyperbolic mappings in length metric spaces. Comptes Rendus. Mathématique, Tome 359 (2021) no. 3, pp. 237-247. doi : 10.5802/crmath.154. http://www.numdam.org/articles/10.5802/crmath.154/

[1] Beurling, Arne; Ahlfors, Lars V. The boundary correspondence under quasiconformal mappings, Acta Math., Volume 96 (1956), pp. 125-142 | DOI | MR | Zbl

[2] Huang, Manzi; Li, Yaxiang; Wang, Xiantao; Zhou, Qingshan Rough quasi-mappings and Gromov hyperbolic spaces (2021) (Submited)

[3] Huang, Manzi; Rasila, Antti; Wang, Xiantao; Zhou, Qingshan Semisolidity and locally weak quasi-symmetry of homeomorphisms in metric spaces, Stud. Math., Volume 242 (2018) no. 3, pp. 267-301 | DOI | Zbl

[4] Huang, Xiaojun; Liu, Hongjun; Liu, Jingsong Local properties of quasi-hyperbolic mappings in metric spaces, Ann. Acad. Sci. Fenn., Math., Volume 41 (2016) no. 1, pp. 23-40 | DOI | Zbl

[5] Rudin, Walter Functional analysis, International Series in Pure and Applied Mathematics, McGraw-Hill, 1991 | Zbl

[6] Sturm, Karl Theodor On the geometry of metric measure spaces. I., Acta Math., Volume 196 (2006) no. 1, pp. 65-131 | DOI | MR | Zbl

[7] Tukia, Pekka; Väisälä, Jussi Quasisymmetric embeddings of metric spaces, Ann. Acad. Sci. Fenn., Math., Volume 5 (1980), pp. 97-114 | DOI | MR | Zbl

[8] Tukia, Pekka; Väisälä, Jussi Lipschitz and quasiconformal approximation and extension, Ann. Acad. Sci. Fenn., Math., Volume 6 (1981), pp. 303-342 | DOI | MR | Zbl

[9] Väisälä, Jussi Free quasiconformality in Banach spaces. I, Ann. Acad. Sci. Fenn., Math., Volume 15 (1990) no. 2, pp. 355-379 | DOI | MR | Zbl

[10] Väisälä, Jussi The free quasiworld, freely quasiconformal and related maps in Banach spaces, Quasiconformal geometry and dynamics (Lublin, 1996) (Banach Center Publications), Volume 48, Polish Academy of Sciences, Institute of Mathematics, 1999, pp. 55-118 | MR | Zbl

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