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Fundam. Prikl. Mat., 2006, Volume 12, Issue 1, Pages 57–94 (Mi fpm923)  

This article is cited in 4 scientific papers (total 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.

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

Bibliographic databases:

UDC: 514.144.23+514.172.45+514.177.2

Citation: N. S. Gusev, “Canonical decompositions of piecewise affine mappings, polyhedra-traces, and geometrical variational problems”, Fundam. Prikl. Mat., 12:1 (2006), 57–94; J. Math. Sci., 149:1 (2008), 896–921

Citation in format AMSBIB
\Bibitem{Gus06}
\by N.~S.~Gusev
\paper Canonical decompositions of piecewise affine mappings, polyhedra-traces, and geometrical variational problems
\jour Fundam. Prikl. Mat.
\yr 2006
\vol 12
\issue 1
\pages 57--94
\mathnet{http://mi.mathnet.ru/fpm923}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2249680}
\zmath{https://zbmath.org/?q=an:1156.57018}
\elib{http://elibrary.ru/item.asp?id=9166885}
\transl
\jour J. Math. Sci.
\yr 2008
\vol 149
\issue 1
\pages 896--921
\crossref{https://doi.org/10.1007/s10958-008-0034-z}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-38349188943}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. O. Ivanov, A. A. Tuzhilin, “Immersed polygons and their diagonal triangulations”, Izv. Math., 72:1 (2008), 63–90  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. A. O. Ivanov, A. A. Tuzhilin, “One-dimensional Gromov minimal filling problem”, Sb. Math., 203:5 (2012), 677–726  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Gusev N.S., “Kriterii kusochno affinnykh smyatii i kontraktsii”, Nauka i obrazovanie: elektronnoe nauchno-tekhnicheskoe izdanie, 2012, no. 11, 11–11  zmath  elib
    4. Ivanov A.O., Tuzhilin A.A., “Gromov Minimal Fillings for Finite Metric Spaces”, Publ. Inst. Math.-Beograd, 94:108 (2013), 3–15  crossref  mathscinet  zmath  isi
  • Фундаментальная и прикладная математика
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