On boundary discreteness of mappings with a modulus condition

We study the boundary behavior of spatial mappings that distort themodulus of families of paths in the same way as the inverse Poletskyinequality. Under certain conditions on the boundaries of thecorresponding domains, we have shown that such mappings have acontinuous boundary extension. Separately, we study the problem ofdiscreteness of the indicated extension. It is shown that undersome requirements, it is light, and under some more strongconditions, it is discrete in the closure of a domain.

Automated summary

This paper studies the boundary behavior of spatial mappings that distort the modulus of families of paths in the same way as the inverse Poletsky inequality. It is shown that under certain conditions on the boundaries of the corresponding domains, such mappings have a continuous boundary extension. Additionally, the discreteness of the indicated extension is also studied, revealing that it is light under certain requirements and discrete in the closure of a domain under stronger conditions.