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

Evgeny Sevost'yanov; Valery Targonskii

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arXiv · 2405.09012

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

Evgeny Sevost'yanov·Valery Targonskii

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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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BibTeX RIS

Evgeny Sevost'yanov, Valery Targonskii. 2024-05-27. An analogue of Koebe's theorem and the openness of a limit map in one class. https://arxiv.org/abs/2405.09012

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