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 [
Citation: Qingtian Shi. Equivalent characterizations of harmonic Teichmüller mappings[J]. AIMS Mathematics, 2022, 7(6): 11015-11023. doi: 10.3934/math.2022615
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 [
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