Geodesic
On diffeomorphic mappings of one nondegenerate parallelepiped onto another
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical Analysis, Tome 155 (2018), pp. 98-114

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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. 
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     author = {S. P. Babenko and A. V. Bad'in},
     title = {On diffeomorphic mappings of one nondegenerate parallelepiped onto another},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {98--114},
     publisher = {mathdoc},
     volume = {155},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_155_a5/}
}
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S. P. Babenko; A. V. Bad'in. On diffeomorphic mappings of one nondegenerate parallelepiped onto another. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical Analysis, Tome 155 (2018), pp. 98-114. http://geodesic.mathdoc.fr/item/INTO_2018_155_a5/