Maximum properties of affine minimal hypersurfaces (Q1311026)

E. Calabi showed that the sign of the second variation of locally strongly convex affine minimal hypersurfaces in affine space \(A^ n\) for \(n\geq 4\) can not be determined by a suitable reduction to a sum of squares as was done for \(n=3\). In this paper, the author proves that strictly stable locally strongly convex affine minimal hypersurfaces are relative weak maxima of the affine area functional, and gives an affine version of the Morse-Smale index theorem.