The logarithmic Minkowski problem

Károly J. Böröczky; Erwin Lutwak; Deane Yang; Gaoyong Zhang

doi:10.1090/S0894-0347-2012-00741-3

The logarithmic Minkowski problem

Károly J. Böröczky, Erwin Lutwak, Deane Yang, Gaoyong Zhang

Mathematics

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

Abstract

In analogy with the classical Minkowski problem, necessary and sufficient conditions are given to assure that a given measure on the unit sphere is the cone-volume measure of the unit ball of a finite-dimensional Banach space.

Original language	English (US)
Pages (from-to)	831-852
Number of pages	22
Journal	Journal of the American Mathematical Society
Volume	26
Issue number	3
DOIs	https://doi.org/10.1090/S0894-0347-2012-00741-3
State	Published - 2013

Keywords

Cone-volume measure
Log-Minkowski problem
Lp-Minkowski problem
Minkowski problem

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0894-0347-2012-00741-3

Cite this

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title = "The logarithmic Minkowski problem",

abstract = "In analogy with the classical Minkowski problem, necessary and sufficient conditions are given to assure that a given measure on the unit sphere is the cone-volume measure of the unit ball of a finite-dimensional Banach space.",

keywords = "Cone-volume measure, Log-Minkowski problem, Lp-Minkowski problem, Minkowski problem",

author = "B{\"o}r{\"o}czky, {K{\'a}roly J.} and Erwin Lutwak and Deane Yang and Gaoyong Zhang",

year = "2013",

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AU - Böröczky, Károly J.

AU - Lutwak, Erwin

AU - Yang, Deane

AU - Zhang, Gaoyong

PY - 2013

Y1 - 2013

N2 - In analogy with the classical Minkowski problem, necessary and sufficient conditions are given to assure that a given measure on the unit sphere is the cone-volume measure of the unit ball of a finite-dimensional Banach space.

AB - In analogy with the classical Minkowski problem, necessary and sufficient conditions are given to assure that a given measure on the unit sphere is the cone-volume measure of the unit ball of a finite-dimensional Banach space.

KW - Cone-volume measure

KW - Log-Minkowski problem

KW - Lp-Minkowski problem

KW - Minkowski problem

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The logarithmic Minkowski problem

Abstract

Keywords

ASJC Scopus subject areas

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