Abstract
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].
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Krauter, P. Maximum properties of affine minimal hypersurfaces. Results. Math. 24, 228–245 (1993). https://doi.org/10.1007/BF03322333
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DOI: https://doi.org/10.1007/BF03322333