[Authors]
 N. M. Ivochkina; N. V. Filimonenkova

[Title]
 Geometrical models in the theory of fully nonlinear differential equations

[AMS Subj-class]
 53A55 Differential invariants (local theory), geometric objects
 35J60 Nonlinear elliptic equations

[Abstract]
 During the development of the modern theory of fully nonlinear differential
 equations of second order there are new algebraic and geometric characteristics.
 Implementation of the geometric characteristics of the language of classical
 differential geometry leads to unnecessary technical difficulties. This work
 contains the review of undertaken methodological reform and demonstrates a new
 differential-geometric models on the example of the construction of boundary
 barriers for Hessian equations.

[Keywords]
 curvature matrix; p-curvature; m-convex hypersurface; m-Hessian equations;
 kernel of boundary barrier

[Comments]
 LaTeX, Russian, 31 pp.

[Contact e-mail]
 ninaiv@NI1570.spb.edu
 nf33@yandex.ru