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.

Location: http://mech.math.msu.su/~fpm/eng/k06/k061/k06102h.htm

Last modified: July 8, 2006