Evolution of Tzitzeica hypersurfaces

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.