具有模条件的映射的边界离散性

Pub Date : 2023-11-01 DOI:10.1007/s10474-023-01381-z

E. Sevost’yanov

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引用次数: 0

摘要

我们研究了扭曲路径族模的空间映射的边界行为，其方式与逆poletsky不等式相同。在相应域边界的一定条件下，我们证明了这种映射具有连续的边界扩展。另外，我们研究了指示扩展的离散性问题。证明了在某些条件下，它是轻的，在一些更强的条件下，它在一个域的闭包中是离散的。

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On boundary discreteness of mappings with a modulus condition

We study the boundary behavior of spatial mappings that distort the modulus of families of paths in the same way as the inverse Poletsky inequality. Under certain conditions on the boundaries of the corresponding domains, we have shown that such mappings have a continuous boundary extension. Separately, we study the problem of discreteness of the indicated extension. It is shown that under some requirements, it is light, and under some more strong conditions, it is discrete in the closure of a domain.

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