Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 155, Pages 98–114 (Mi into392)  
On diffeomorphic mappings of one nondegenerate parallelepiped onto another

S. P. Babenkoa, A. V. Bad'inb

a Bauman Moscow State Technical University
b Lomonosov Moscow State University
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Abstract: In this paper, we consider diffeomorphic mappings of a nondegenerate parallelepiped onto another such parallelepiped. We prove that the image of any face of the first parallelepiped under such a mapping is a certain face of the second parallelepiped. Moreover, we also obtain several auxiliary results on the transformation of boundary points of a nondegenerate parallelepiped under the action of a diffeomorphism.
Keywords: homeomorphism, diffeomorphism, boundary of a set, parallelepiped.
English version:
Journal of Mathematical Sciences (New York), 2021, Volume 254, Issue 5, Pages 686–702
DOI: https://doi.org/10.1007/s10958-021-05333-2
Bibliographic databases:
Document Type: Article
UDC: 514.7
MSC: 26B05
Language: Russian
Citation: S. P. Babenko, A. V. Bad'in, “On diffeomorphic mappings of one nondegenerate parallelepiped onto another”, Mathematical Analysis, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 155, VINITI, Moscow, 2018, 98–114; J. Math. Sci. (N. Y.), 254:5 (2021), 686–702
Citation in format AMSBIB
\Bibitem{BabBad18}
\by S.~P.~Babenko, A.~V.~Bad'in
\paper On diffeomorphic mappings of one nondegenerate parallelepiped onto another
\inbook Mathematical Analysis
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 155
\pages 98--114
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into392}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=3904907}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2021
\vol 254
\issue 5
\pages 686--702
\crossref{https://doi.org/10.1007/s10958-021-05333-2}
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