An analogue of Koebe's theorem and the openness of a limit map in one class

2024/05/15 by Sevost'yanov, Evgeny, Targonskii, Valery · 4 citations
#30C65 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2405.09012

Abstract

We study mappings that satisfy the inverse modulus inequality of Poletsky type in a fixed domain. It is shown that, under some additional restrictions, the image of a ball under such mappings contains a fixed ball uniformly over the class. This statement can be interpreted as the well-known analogue of Koebe's theorem for analytic functions. As an application of the obtained result, we show that, if a sequence of mappings belonging to the specified class converges locally uniformly, then the limit mapping is open.

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• An analogue of Koebe's theorem in metric spaces
• On Koebe's theorem for mappings with integral constraints
• On equicontinuity of mappings with inverse moduli inequalities by prime ends of variable domains
• On uniformly lightness of ring mappings and convergence to a homeomorphism

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