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 and a number ρ ≥ 0, the outer parallel body of K at distance ρ is the set
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 ...