ISOPERIMETRIC INEQUALITIES FOR INTEGRAL GEOMETRIC INVARIANTS OF RANDOM LINES

doi:10.1007/s10473-025-0115-9

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (1): 189-199.doi: 10.1007/s10473-025-0115-9

ISOPERIMETRIC INEQUALITIES FOR INTEGRAL GEOMETRIC INVARIANTS OF RANDOM LINES

Gaoyong Zhang

Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, 251. Mercer Street, New York, NY 10012, USA

收稿日期:2024-09-03 发布日期:2025-02-06
作者简介:Gaoyong Zhang, E-mail,: gaoyong.zhang@courant.nyu.edu
基金资助:
The research was supported, in part, by the NSF Grant DMS-2005875.

ISOPERIMETRIC INEQUALITIES FOR INTEGRAL GEOMETRIC INVARIANTS OF RANDOM LINES

Gaoyong Zhang

Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, 251. Mercer Street, New York, NY 10012, USA

Received:2024-09-03 Published:2025-02-06
About author:Gaoyong Zhang, E-mail,: gaoyong.zhang@courant.nyu.edu
Supported by:
The research was supported, in part, by the NSF Grant DMS-2005875.

摘要/Abstract

摘要： 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.

关键词: isoperimetric inequality, convex body, random points, random lines, chord integral, Riesz potential, entropy

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

中图分类号:

52A40

Gaoyong Zhang. ISOPERIMETRIC INEQUALITIES FOR INTEGRAL GEOMETRIC INVARIANTS OF RANDOM LINES[J]. 数学物理学报(英文版), 2025, 45(1): 189-199.

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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ISOPERIMETRIC INEQUALITIES FOR INTEGRAL GEOMETRIC INVARIANTS OF RANDOM LINES

ISOPERIMETRIC INEQUALITIES FOR INTEGRAL GEOMETRIC INVARIANTS OF RANDOM LINES

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