Displaying similar documents to “Illumination bodies and affine surface area”

A general geometric construction for affine surface area

Elisabeth Werner (1999)

Studia Mathematica

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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 → 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 ≥ 0 , B t t ≥ 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].