[Authors]
 Filimonenkova, N. V.; Bakusov, P. A.

[Title]
 Analysis of m-convexity of multydimensional paraboloids and hyperboloids

[AMS Subj-class]
 53A07 Higher-dimensional and -codimensional surfaces in Euclidean $n$-space
 53C45 Global surface theory (convex surfaces a la A. D. Aleksandrov)

[Abstract]
 The work is dedicated to a new notion in the differential geometry: m-convex
 hypersurface. This notion is a generalization of the classical convexity.
 It appeared at the end of the XX century as a result of a successful
 application of Garding's cones in the theory of fully nonlinear differential
 equations in partial derivatives. The authors briefly describe the notion of
 m-convex hypersurfaces and study m-convexity of multidimensional quadrics:
 paraboloids and hyperboloids. The results are illustrated in 2-dimensional
 and 3-dimensional quadrics.

[Keywords]
 p-curvature, m-convex surface, paraboloid, hyperboloid, domain of m-convexity,
 Garding's cones

[Comments]
 LaTeX, Russian, 22 pp.
 The paper was accepted for publication in the journal «Математическое просвещение».

[Contact e-mail]
 nf33@yandex.ru