Evolution of Tzitzeica hypersurfaces

Autori

  • Constantin Udrişte University Politehnica of Bucharest
  • Ionel Țevy University Politehnica of Bucharest
  • Ali Sapeeh Rasheed University Politehnica of Bucharest

DOI:

https://doi.org/10.1478/AAPP.961A7

Parole chiave:

Tzitzeica hypersurface, convexity, geometric evolution ODEs and PDEs

Abstract

Our aim is to study the evolutions of Tzitzeica hypersurfaces which appear in understanding the dynamics of some geometric programming problems and reliability optimal allocation problems. Section 2 analyses the convexity of a Tzitzeica hypersurface. Sections 3-6 refer to standard Tzitzeica hypersurfaces and their evolutions by convenient geometrical flows: (i) evolution along the normal vector field, (ii) infinitesimal normal transformation of a Tzitzeica hypersurface, (iii) evolution along a centro affine vector field, and (iv) evolution along an affine vector field. Sections 7-8 include results on the Tzitzeica law in economics and the evolution of Tzitzeica surfaces described by PDEs: (v) Tzitzeica hypersurfaces as invariants w.r.t. excess demand flow; (vi) parametric Tzitzeica surfaces based on PDEs and their evolutions.

Dowloads

Pubblicato

2018-06-22

Fascicolo

V. 96 N. 1 (2018)

Sezione

Articoli

Licenza

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