The log-Brunn-Minkowski inequality

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

doi:10.1016/j.aim.2012.07.015

The log-Brunn-Minkowski inequality

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

Mathematics

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

Abstract

For origin-symmetric convex bodies (i.e., the unit balls of finite dimensional Banach spaces) it is conjectured that there exist a family of inequalities each of which is stronger than the classical Brunn-Minkowski inequality and a family of inequalities each of which is stronger than the classical Minkowski mixed-volume inequality. It is shown that these two families of inequalities are "equivalent" in that once either of these inequalities is established, the other must follow as a consequence. All of the conjectured inequalities are established for plane convex bodies.

Original language	English (US)
Pages (from-to)	1974-1997
Number of pages	24
Journal	Advances in Mathematics
Volume	231
Issue number	3-4
DOIs	https://doi.org/10.1016/j.aim.2012.07.015
State	Published - Oct 2012

Keywords

Brunn-Minkowski inequality
Brunn-Minkowski-Firey inequality
Minkowski mixed-volume inequality
Minkowski-Firey L -combinations

ASJC Scopus subject areas

General Mathematics

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10.1016/j.aim.2012.07.015

Cite this

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AU - Böröczky, Károly J.

AU - Lutwak, Erwin

AU - Yang, Deane

AU - Zhang, Gaoyong

N1 - Funding Information: Research of first named author supported, in part, by Grant OTKA 075016 . Research of the other three authors supported, in part, by NSF Grant DMS-1007347 .

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KW - Brunn-Minkowski inequality

KW - Brunn-Minkowski-Firey inequality

KW - Minkowski mixed-volume inequality

KW - Minkowski-Firey L -combinations

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The log-Brunn-Minkowski inequality

Abstract

Keywords

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