Stability of the Graph of a Convex Function

Let x: M → A ⁿ⁺¹ be the graph of some strongly convex function x ⁿ+1= ?( x₁,…,x_n) defined on a domain Ω ? A ⁿ in a real affine space. We consider the relative metric G, defined by $ G=\sum{\partial^{2}f\over\partial x_{i}\partial x_{j}}dx_{i}dx_{j}$ .In this paper, we calculate the second variation of the area integral with respect to the relative metric G. We prove that the parabolic affine hyperspheres are stable.