The Brunn-Minkowski inequality, Minkowski's first inequality and their duals

R. J. Gardner; Salvatore Flavio Vassallo

doi:10.1006/jmaa.2000.6774

The Brunn-Minkowski inequality, Minkowski's first inequality and their duals

R. J. Gardner, Salvatore Flavio Vassallo

Western Washington University

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

9 Citations (Scopus)

Abstract

Quantitative versions are given of the equivalence of the Brunn-Minkowski inequality and Minkowski's first inequality from the Brunn-Minkowski theory. Similar quantitative versions are obtained of the equivalence of the corresponding inequalities from Lutwak's dual Brunn-Minkowski theory. The main results are shown to be the best possible up to constant factors.

Original language	English
Pages (from-to)	502-512
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
DOIs	https://doi.org/10.1006/jmaa.2000.6774
Publication status	Published - 2000

Keywords

Brunn-Minkowski inequality
Convex body
dual Brunn-Minkowski inequality
geometric tomography
star body

Access to Document

10.1006/jmaa.2000.6774

Cite this

@article{a7aa92e3bc4d42899f2ee4f9f85b14fb,

title = "The Brunn-Minkowski inequality, Minkowski's first inequality and their duals",

abstract = "Quantitative versions are given of the equivalence of the Brunn-Minkowski inequality and Minkowski's first inequality from the Brunn-Minkowski theory. Similar quantitative versions are obtained of the equivalence of the corresponding inequalities from Lutwak's dual Brunn-Minkowski theory. The main results are shown to be the best possible up to constant factors.",

keywords = "Brunn-Minkowski inequality, Convex body, dual Brunn-Minkowski inequality, geometric tomography, star body, Brunn-Minkowski inequality, Convex body, dual Brunn-Minkowski inequality, geometric tomography, star body",

author = "Gardner, {R. J.} and Vassallo, {Salvatore Flavio}",

year = "2000",

doi = "10.1006/jmaa.2000.6774",

language = "English",

pages = "502--512",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Incorporated:6277 Sea Harbor Drive:Orlando, FL 32887:(800)543-9534, (407)345-4100, EMAIL: ap@acad.com, INTERNET: http://www.idealibrary.com, Fax: (407)352-3445",

}

TY - JOUR

T1 - The Brunn-Minkowski inequality, Minkowski's first inequality and their duals

AU - Gardner, R. J.

AU - Vassallo, Salvatore Flavio

PY - 2000

Y1 - 2000

N2 - Quantitative versions are given of the equivalence of the Brunn-Minkowski inequality and Minkowski's first inequality from the Brunn-Minkowski theory. Similar quantitative versions are obtained of the equivalence of the corresponding inequalities from Lutwak's dual Brunn-Minkowski theory. The main results are shown to be the best possible up to constant factors.

AB - Quantitative versions are given of the equivalence of the Brunn-Minkowski inequality and Minkowski's first inequality from the Brunn-Minkowski theory. Similar quantitative versions are obtained of the equivalence of the corresponding inequalities from Lutwak's dual Brunn-Minkowski theory. The main results are shown to be the best possible up to constant factors.

KW - Brunn-Minkowski inequality

KW - Convex body

KW - dual Brunn-Minkowski inequality

KW - geometric tomography

KW - star body

KW - Brunn-Minkowski inequality

KW - Convex body

KW - dual Brunn-Minkowski inequality

KW - geometric tomography

KW - star body

UR - http://hdl.handle.net/10807/29401

U2 - 10.1006/jmaa.2000.6774

DO - 10.1006/jmaa.2000.6774

M3 - Article

SN - 0022-247X

SP - 502

EP - 512

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

ER -

The Brunn-Minkowski inequality, Minkowski's first inequality and their duals

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this