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Convex Bodies: The Brunn–Minkowski Theory, Second Edition by Rolf Schneider

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4

Support measures and intrinsic volumes

With this chapter, we start a detailed study of functionals on convex bodies, such as volume, surface area, functionals derived from them and measures related to them. The investigation of inequalities for such functionals will begin with Chapter 7.

4.1 Local parallel sets

Recall that for a convex body image and a number ρ ≥ 0, the outer parallel body of K at distance ρ is the set

image

The Steiner formula (to be proved in Section 4.2) says that its volume can be expressed as a polynomial of degree at most n in the ...

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