Curvature Measures of Singular Sets by Jan Rataj & Martina Zähle

Author:Jan Rataj & Martina Zähle
Language: eng
Format: epub
ISBN: 9783030181833
Publisher: Springer International Publishing

for any bounded Borel set .

Remark 6.25

1.If X is a convex body then all principal curvatures are nonnegative, the absolute value in the formula can be omitted and we can can integrate (see Example 1.​18)

Thus, we obtain in this case, cf. Definition 4.​28.

2.Using the inequality for the inner integral over the Grassmannian, we obtain

Example 6.26

Let X be a full-dimensional body in with sufficiently smooth boundary, and let κ 1(x), κ 2(x) be the principal curvatures, x ∈ ∂X. Then

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