Evolution of Tzitzeica hypersurfaces

Authors

  • 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

Keywords:

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.

Downloads

Published

2018-06-22

Issue

Vol. 96 No. 1 (2018)

Section

Articles

License

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

Authors who publish with this journal agree to the following terms:
  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).