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Integral geometry of pairs of hyperplanes or lines
Archiv der Mathematik ( IF 0.6 ) Pub Date : 2020-04-13 , DOI: 10.1007/s00013-020-01465-0
Daniel Hug , Rolf Schneider

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.

中文翻译:

超平面或线对的积分几何

Crofton 的积分几何公式评估与给定凸体具有非空交点的 k 维平面集的总运动不变测度。本注释涉及对与凸体相交的超平面或直线对的集合的运动不变性测度。当且仅当给定的物体在第一种情况下具有恒定的宽度,在第二种情况下具有恒定的亮度时,才能获得特别简单的结果。
更新日期:2020-04-13
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