For ball-bodies, the c-affine surface area is maximized by the ball of radius n/(n+1), and the product with its c-dual is bounded by the squared value at the ball of radius 1/2.
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Some inequalities of isoperimetric type for the c-affine surface area
For ball-bodies, the c-affine surface area is maximized by the ball of radius n/(n+1), and the product with its c-dual is bounded by the squared value at the ball of radius 1/2.