A general geometric construction for affine surface area

Volume 132 / 1999

Elisabeth Werner Studia Mathematica 132 (1999), 227-238 DOI: 10.4064/sm-132-3-227-238

Abstract

Let K be a convex body in $ℝ^n$ and B be the Euclidean unit ball in $ℝ^n$. We show that $lim_{t→ 0} (|K| -|K_t|)/(|B| - |B_t|) = as(K)/as(B)$, 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].

Authors

  • Elisabeth Werner

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