Isoperimetric inequalities for integral geometric invariants of random lines

Gaoyong Zhang

doi:10.1007/s10473-025-0115-9

Isoperimetric inequalities for integral geometric invariants of random lines

Gaoyong Zhang

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	189-199
Number of pages	11
Journal	Acta Mathematica Scientia
Volume	45
Issue number	1
DOIs	https://doi.org/10.1007/s10473-025-0115-9
State	Published - Jan 2025

Keywords

52A22
52A40
chord integral
convex body
entropy
isoperimetric inequality
random lines
random points
Riesz potential

ASJC Scopus subject areas

General Mathematics
General Physics and Astronomy

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10.1007/s10473-025-0115-9

Cite this

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title = "Isoperimetric inequalities for integral geometric invariants of random lines",

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.",

keywords = "52A22, 52A40, chord integral, convex body, entropy, isoperimetric inequality, random lines, random points, Riesz potential",

author = "Gaoyong Zhang",

note = "Publisher Copyright: {\textcopyright} Innovation Academy for Precision Measurement Science and Technology, Chinese Academy of Sciences 2025.",

year = "2025",

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AB - 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.

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KW - convex body

KW - entropy

KW - isoperimetric inequality

KW - random lines

KW - random points

KW - Riesz potential

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Isoperimetric inequalities for integral geometric invariants of random lines

Abstract

Keywords

ASJC Scopus subject areas

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