On Busemann surface area of the unit ball in Minkowski spaces.

Mustafaev, Zokhrab

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Let K be a convex body in $ℝ^{n}$ and B be the Euclidean unit ball in $ℝ^{n}$ . We show that $l i m_{t \to 0} (| K | - | K_{t} |) / (| B | - | B_{t} |) = a s (K) / a s (B)$ , where as(K) respectively as(B) is the affine surface area of K respectively B and ${K_{t}}_{t \geq 0}$ , ${B_{t}}_{t \geq 0}$ are general families of convex bodies constructed from K,B satisfying certain conditions. As a corollary we get results obtained in [M-W], [Schm], [S-W] and [W].