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

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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.

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Authors and Affiliations

  1. Bauman Moscow State Technical University, Russia

    N. S. Gusev

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  1. N. S. Gusev
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Correspondence to N. S. Gusev.

Additional information

This research was partially supported by RF President’s grants NSh-1988.2003.1 and MD-263.2003.01.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 1, pp. 57–94, 2006.

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Gusev, N.S. Canonical decompositions of piecewise affine mappings, polyhedra-traces, and geometrical variational problems. J Math Sci 149, 896–921 (2008). https://doi.org/10.1007/s10958-008-0034-z

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  • DOI: https://doi.org/10.1007/s10958-008-0034-z

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