Evolution of Tzitzeica hypersurfaces

Constantin Udrişte, Ionel Țevy, Ali Sapeeh Rasheed

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.

Keywords


Tzitzeica hypersurface; convexity; geometric evolution ODEs and PDEs

Full Text:

PDF


DOI: http://dx.doi.org/10.1478/AAPP.961A7

Copyright (c) 2018 Constantin Udriste

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.