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Projection bodies in complex vector spaces

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jun 2011Embargo end date: 01 Jan 2011Publisher:Elsevier BVJournal:Advances in Mathematics, volume 227, pages 830-846 (issn: 0001-8708, Copyright policy )
Authors: Judit Abardia; Andreas Bernig;

doi: 10.1016/j.aim.2011.02.013 , 10.48550/arxiv.1101.5927

arXiv: http://arxiv.org/abs/1101.5927

Projection bodies in complex vector spaces

Abstract

The space of Minkowski valuations on an m-dimensional complex vector space which are continuous, translation invariant and contravariant under the complex special linear group is explicitly described. Each valuation with these properties is shown to satisfy geometric inequalities of Brunn-Minkowski, Aleksandrov-Fenchel and Minkowski type.

20 pages, minor changes, to appear in Adv. Math

Related Organizations
Keywords

Brunn–Minkowski inequality, Mathematics - Differential Geometry, Mathematics(all), Differential Geometry (math.DG), Projection body, Minkowski valuation, FOS: Mathematics, Convex bodies, 52B45, 52A39, 52A40

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
70
Top 10%
Top 10%
Top 10%
Green
hybrid