Abstract:<abstract><p>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 <sup>[<xref ref-type="bibr" rid="b1">1</xref>]</sup>. Furthermore, the representation theorem of $ 1/|\omega|^{2} $-harmonic Teichmüller mappings is… Show more
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