Stability Of The Graph Of A Convex Function

In Chapter 1, we introduce the context of the paper and draw the conclusion. In Chapter 2, we introduce the relative metric of the hypersurface in the relative affine differential geometry. We study the Fubini-Pick form and Pick invariant. In Chapter 3, let x : M → An+l be the graph of some strictly convex functionxn+1 = /(x1,..... ,xn), defined in a domain An. We consider the relative metric G, defined byIn this paper, we calculate the second variation of area integral with respect to the relative metric G, and we can prove that the parabolic affine hyperspheres are stable.