Equivalent characterizations of harmonic Teichmüller mappings

Qingtian Shi; Qingtian Shi

doi:10.3934/math.2022615

AIMS Mathematics

2022, Volume 7, Issue 6: 11015-11023. doi: 10.3934/math.2022615

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Research article

Equivalent characterizations of harmonic Teichmüller mappings

Qingtian Shi ^,

School of Mathematics, Quanzhou Normal University, 362000, Fujian, China

Received: 22 January 2022 Revised: 17 March 2022 Accepted: 27 March 2022 Published: 06 April 2022
MSC : Primary 30C62; Secondary 31A05, 31A35

In this paper, three equivalent conditions of $ \rho $-harmonic Teichmüller mapping are given firstly. As an application, we investigate the relationship between a $ \rho $-harmonic Teichmüller mapping and its associated holomorphic quadratic differential and obtain a relatively simple method to prove Theorem 2.1 in ^[1]. Furthermore, the representation theorem of $ 1/|\omega|^{2} $-harmonic Teichmüller mappings is given as a by-product. Our results extend the corresponding researches of harmonic Teichmüller mappings.
- flat harmonic mapping,
- Teichmüller mapping,
- associated holomorphic quadratic differential,
- quasiconformal mapping
Citation: Qingtian Shi. Equivalent characterizations of harmonic Teichmüller mappings[J]. AIMS Mathematics, 2022, 7(6): 11015-11023. doi: 10.3934/math.2022615

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Abstract

In this paper, three equivalent conditions of $ \rho $-harmonic Teichmüller mapping are given firstly. As an application, we investigate the relationship between a $ \rho $-harmonic Teichmüller mapping and its associated holomorphic quadratic differential and obtain a relatively simple method to prove Theorem 2.1 in ^[1]. Furthermore, the representation theorem of $ 1/|\omega|^{2} $-harmonic Teichmüller mappings is given as a by-product. Our results extend the corresponding researches of harmonic Teichmüller mappings.

References

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