This article is cited in 4 papers

Canonical decompositions of piecewise affine mappings, polyhedra-traces, and geometrical variational problems

N. S. Gusev

N. E. Bauman Moscow State Technical University

Abstract: 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.

UDC: 514.144.23+514.172.45+514.177.2

 English version: Journal of Mathematical Sciences (New York), 2008, 149:1, 896–921

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