Illumination bodies and affine surface area
Volume 110 / 1994
Studia Mathematica 110 (1994), 257-269
DOI: 10.4064/sm-110-3-257-269
Abstract
We show that the affine surface area as(∂K) of a convex body K in $ℝ^{n}$ can be computed as $as(∂K) = lim_{δ→0} d_{n} (vol_{n}(K^{δ}) - vol_{n}(K))/(δ^{2/(n+1)})$ where $d_{n}$ is a constant and $K^{δ}$ is the illumination body.
