Busemann–Petty problem
In the mathematical field of convex geometry, the Busemann–Petty problem, introduced by Herbert Busemann and , asks whether it is true that a symmetric convex body with larger central hyperplane sections has larger volume. More precisely, if K, T are symmetric convex bodies in Rn such that for every hyperplane A passing through the origin, is it true that Voln K ≤ Voln T? Busemann and Petty showed that the answer is positive if K is a ball. In general, the answer is positive in dimensions at most 4, and negative in dimensions at least 5.
Wikipage redirect
Link from a Wikipage to another Wikipage
primaryTopic
Busemann–Petty problem
In the mathematical field of convex geometry, the Busemann–Petty problem, introduced by Herbert Busemann and , asks whether it is true that a symmetric convex body with larger central hyperplane sections has larger volume. More precisely, if K, T are symmetric convex bodies in Rn such that for every hyperplane A passing through the origin, is it true that Voln K ≤ Voln T? Busemann and Petty showed that the answer is positive if K is a ball. In general, the answer is positive in dimensions at most 4, and negative in dimensions at least 5.
has abstract
In the mathematical field of c ...... tive in dimensions at least 5.
@en
Задача Буземана — Петти — вопр ...... рналов, Annals of Mathematics.
@ru
Link from a Wikipage to an external page
Wikipage page ID
33,294,058
page length (characters) of wiki page
Wikipage revision ID
1,020,579,661
Link from a Wikipage to another Wikipage
author2-link
Claude Ambrose Rogers
@en
Clinton Myers Petty
@en
authorlink
Herbert Busemann
@en
b
n
@en
doi
1.02307e+1
first
A.
@en
Claude Ambrose
@en
Clinton Myers
@en
Herbert
@en
Richard J.
@en
T.
@en
journal
last
Busemann
@en
Gardner
@en
Koldobsky
@en
Larman
@en
Petty
@en
Rogers
@en
Schlumprecht
@en
loc
problem 1
@en
mr
p
p
@en
series
Second Series
@en
title
An analytic solution to the Busemann-Petty problem on sections of convex bodies
@en
wikiPageUsesTemplate
year
subject
comment
In the mathematical field of c ...... tive in dimensions at least 5.
@en
Задача Буземана — Петти — вопр ...... рналов, Annals of Mathematics.
@ru
label
Busemann–Petty problem
@en
Задача Буземана — Петти
@ru