Integral geometry of pairs of hyperplanes or lines

Daniel Hug; Rolf Schneider

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arXiv · 1911.11659

Integral geometry of pairs of hyperplanes or lines

Daniel Hug·Rolf Schneider

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Abstract

Crofton's formula of integral geometry evaluates the total motion invariant measure of the set of $k$-dimensional planes having nonempty intersection with a given convex body. This note deals with motion invariant measures on sets of pairs of hyperplanes or lines meeting a convex body. Particularly simple results are obtained if, and only if, the given body is of constant width in the first case, and of constant brightness in the second case.

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Daniel Hug, Rolf Schneider. 2019-11-26. Integral geometry of pairs of hyperplanes or lines. https://arxiv.org/abs/1911.11659

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