FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2006, VOLUME 12, NUMBER 1, PAGES 57-94

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

N. S. Gusev

Abstract

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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.

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Last modified: July 8, 2006