ISOPERIMETRIC INEQUALITIES FOR INTEGRAL GEOMETRIC INVARIANTS OF RANDOM LINES

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doi:10.1007/s10473-025-0115-9

Abstract: Isoperimetric type inequalities for integral geometric invariants of random lines in the Euclidean space are shown. Entropy inequalities of probability densities on the affine Grassmann manifold of lines are given.

Key words: isoperimetric inequality, convex body, random points, random lines, chord integral, Riesz potential, entropy

CLC Number:

52A40

Gaoyong Zhang. ISOPERIMETRIC INEQUALITIES FOR INTEGRAL GEOMETRIC INVARIANTS OF RANDOM LINES[J].Acta mathematica scientia,Series B, 2025, 45(1): 189-199.

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