On equicontinuity of families of mappings between Riemannian surfaces with respect to prime ends

  • E. Sevost'yanov <p>Zhytomyr Ivan Franko State University, Bol'shaya Berdichevskaya Str., 40, Zhytomyr, 10 008, UKRAINE; Institute of Applied Mathematics and Mechanics of NAS of Ukraine, Dobrovo'skogo Str., 1,&nbsp;Slavyansk, 84 100,&nbsp;&nbsp;UKRAINE</p><p>&nbsp;</p> https://orcid.org/0000-0001-7892-6186
  • O. P. Dovhopiatyi Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine
  • N. S. Ilkevych Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine
  • V. P. Kalenska Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine

Анотація

Given a domain of some Riemannian surface,
we consider questions related to the possibility of a continuous
extension to the boundary of one class of Sobolev mappings. It is
proved that such maps have a continuous boundary extension in terms
of prime ends, and under some additional restrictions their families
are equicontinuous at inner and boundary points of the domain. We
have separately considered the cases of homeomorphisms and mappings
with branching.

Біографії авторів

E. Sevost'yanov, <p>Zhytomyr Ivan Franko State University, Bol'shaya Berdichevskaya Str., 40, Zhytomyr, 10 008, UKRAINE; Institute of Applied Mathematics and Mechanics of NAS of Ukraine, Dobrovo'skogo Str., 1,&nbsp;Slavyansk, 84 100,&nbsp;&nbsp;UKRAINE</p><p>&nbsp;</p>

Profeesor of Math. Analysis Dept. of Zhytomyr Ivan Franko State University; Leading Researcher of Function Theory Dept., Institute of Applied Mathematics and Mechanics of NAS of Ukraine 

O. P. Dovhopiatyi, Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine

Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine

N. S. Ilkevych, Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine

Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine

V. P. Kalenska, Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine

Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine

Посилання

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Опубліковано
2022-06-27
Як цитувати
Sevost’yanov, E., Dovhopiatyi, O. P., Ilkevych, N. S., & Kalenska, V. P. (2022). On equicontinuity of families of mappings between Riemannian surfaces with respect to prime ends. Математичні студії, 57(2), 157-171. https://doi.org/10.30970/ms.57.2.157-171
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