Canonical decompositions of piecewise affine mappings, polyhedra-traces, and geometrical variational problems
Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 1, pp. 57-94
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In this paper, canonical decompositions of arbitrary piecewise affine mappings are constructed. Then the equivalence of these mappings is introduced and the concept of polyhedron-trace is defined as an equivalence class. Finally, the concepts of the volume and the deformation of polyhedra-traces are introduced, the continuity of the volume is proved, and the formula of first variation is obtained. These concepts give an analog of the Plateau principles.
@article{FPM_2006_12_1_a1,
author = {N. S. Gusev},
title = {Canonical decompositions of piecewise affine mappings, polyhedra-traces, and geometrical variational problems},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {57--94},
publisher = {mathdoc},
volume = {12},
number = {1},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2006_12_1_a1/}
}
TY - JOUR AU - N. S. Gusev TI - Canonical decompositions of piecewise affine mappings, polyhedra-traces, and geometrical variational problems JO - Fundamentalʹnaâ i prikladnaâ matematika PY - 2006 SP - 57 EP - 94 VL - 12 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FPM_2006_12_1_a1/ LA - ru ID - FPM_2006_12_1_a1 ER -
%0 Journal Article %A N. S. Gusev %T Canonical decompositions of piecewise affine mappings, polyhedra-traces, and geometrical variational problems %J Fundamentalʹnaâ i prikladnaâ matematika %D 2006 %P 57-94 %V 12 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/FPM_2006_12_1_a1/ %G ru %F FPM_2006_12_1_a1
N. S. Gusev. Canonical decompositions of piecewise affine mappings, polyhedra-traces, and geometrical variational problems. Fundamentalʹnaâ i prikladnaâ matematika, Tome 12 (2006) no. 1, pp. 57-94. http://geodesic.mathdoc.fr/item/FPM_2006_12_1_a1/