On the infinity-norm of the cubic form of complete hyperbolic affine hyperspheres

Roland Hildebrand (1)

1 CASYS - Calculs Algébriques et Systèmes Dynamiques

Let Mn⊂Rn+1 be a complete hyperbolic affine hypersphere with mean curvature H, H<0 , and let C be its cubic form. We derive a differential inequality and an upper bound on the scalar function ||C||∞ defined by the fiber-wise maximum of the value of C on the unit sphere bundle of M. The bounds are attained for the affine hyperspheres which are asymptotic to a simplicial cone. The results have applications in conic optimization.

Mots clés: Affine hypersphere; cubic form; differential inequality

Domaines: Optimisation et contrôle [math.OC]

Roland Hildebrand. On the infinity-norm of the cubic form of complete hyperbolic affine hyperspheres. Results in mathematics = Resultate der Mathematik, 2013, 64 (1-2), pp.113-119. ⟨10.1007/s00025-012-0301-7⟩. ⟨hal-00944369⟩