Affine minimal hypersurfaces of rotation (Q1336250)

A complete list of affine minimal surfaces in \(A^ 3\) with Euclidean rotational symmetry is given. It is proved that these surfaces have maximal affine surface area within the class of all affine surfaces of rotation satisfying suitable boundary conditions. Furthermore, it is shown that for rotationally symmetric locally strongly convex affine minimal hypersurfaces in \(A^ n\), \(n \geq 4\), the second variation of the affine surface area is negative definite under certain conditions on the meridian.