Maximum properties of affine minimal hypersurfaces

It is shown that the sign of the second variation of locally strongly convex affine minimal hypersurfaces in affine space A ⁿ for n ≥ 4 can not be determined by a suitable reduction to a sum of squares as was done for n = 3 in 3]. Also we prove that strictly stable locally strongly convex affine minimal hypersurfaces are a relative weak maximum of the affine area functional, and give an affine version of the Morse-Smale index theorem 16].