Abstract
We provide conditions on the complex dilatation of a homeomorphismf of the upper half plane ℍ into ℂ, which guarantee thatf(ℍ) is a proper subset of ℂ and, in case wheref(ℍ) is a Jordan domain, thatf has a homeomorphic extension onto\(\bar {\mathbb{H}}\).
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Srebro, U., Yakubov, E. Boundary behavior ofμ-homeomorphisms. Isr. J. Math. 141, 249–261 (2004). https://doi.org/10.1007/BF02772222
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DOI: https://doi.org/10.1007/BF02772222