From Gårding's cones to \(p\)-convex hypersurfaces (Q2259057)

The present article is based upon the celebrated paper of \textit{L. Gårding} [J. Math. Mech. 8, 957--965 (1959; Zbl 0090.01603)], in particular the notions of an \(a\)-hyperbolic polynomial and the so-called Gårding cone. The author investigates the Gårding cone related with an \(\mathrm{id}\)-hyperbolic polynomial on the space of symmetric \(n\times n\) matrices. As an application, a class of convex hypersurfaces in \({\mathbb R}^{n+1}\) is investigated in terms of a curvature matrix.