On mean curvature integrals of the outer parallel body of the projection of a convex body. (English) Zbl 1335.52016
Summary: In this paper, we obtain expressions of the mean curvature integrals of two outer parallel bodies, where the outer parallel bodies are in the distance \(\rho\) of a projection body in different space (\(\mathbb R^n\) and \(L_{r[O]}\)). These mean curvature integrals are the generalizations of Santaló’s results. As corollaries, we establish mean values of the mean curvature integrals and Minkowski quermassintegrals of two outer parallel bodies, respectively.
MSC:
| 52A22 | Random convex sets and integral geometry (aspects of convex geometry) |
| 53C65 | Integral geometry |
References:
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