Illumination bodies and affine surface area

ArticleOriginal scientific text

Title

Authors ^1,²

Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106, U.S.A.
Université de Lille 1, U.F.R. de Mathematiques, 59655 Villeneuve d'Ascq, France

We show that the affine surface area as(∂K) of a convex body K in

ℝ^{n}

can be computed as

a s (\partial K) = lim_{δ \to 0} d_{n} \frac{v o l_{n} (K^{δ}) - v o l_{n} (K)}{δ^{\frac{2}{n + 1}}}

where

d_{n}

is a constant and

K^{δ}

is the illumination body.

[B] W. Blaschke, Vorlesungen über Differentialgeometrie II, Springer, 1923.
[H] R. Howard, personal communication.
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