The φ-Brunn–Minkowski inequality

For strictly increasing concave functions φ whose inverse functions are log-concave, the φ -Brunn–Minkowski inequality for planar convex bodies is established. It is shown that for convex bodies in R n the φ -Brunn–Minkowski is equivalent to the φ -Minkowski mixed volume inequalities.

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Bibliographische Detailangaben
Veröffentlicht in:	Acta mathematica Hungarica 2018-10, Vol.156 (1), p.226-239
1. Verfasser:	Lv, S.-J.
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics Mathematics and Statistics
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	For strictly increasing concave functions φ whose inverse functions are log-concave, the φ -Brunn–Minkowski inequality for planar convex bodies is established. It is shown that for convex bodies in R n the φ -Brunn–Minkowski is equivalent to the φ -Minkowski mixed volume inequalities.
ISSN:	0236-5294 1588-2632
DOI:	10.1007/s10474-018-0825-8