Projection bodies in complex vector spaces
Judit Abardia,Andreas Bernig +1 more
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TLDR
In this paper, 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.About:
This article is published in Advances in Mathematics.The article was published on 2011-06-01 and is currently open access. It has received 97 citations till now. The article focuses on the topics: Minkowski space & Minkowski's theorem.read more
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The Centro-Affine Hadwiger Theorem
TL;DR: In this article, all upper semicontinuous and SL(n) invariant valuations on convex bodies containing the origin in their interiors are completely classified, and each such valuation is shown to be a linear combination of the Euler characteristic, the volume, volume of the polar body, and the recently discovered Orlicz surface areas.
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Harmonic Analysis of Translation Invariant Valuations
TL;DR: In this paper, the authors decompose the space of continuous and translation-invariant tensor valuations into a sum of SO(n) irreducible subspaces.
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Harmonic analysis of translation invariant valuations
TL;DR: In this article, the authors decompose the space of continuous and translation invariant tensor valuations into a sum of SO(n) irreducible subspaces, and prove new inequalities of Brunn-Minkowski type for convex body valued valuations.
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()-contravariant _{}-Minkowski valuations
References
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Book
Convex bodies : the Brunn-Minkowski theory
TL;DR: Inequalities for mixed volumes 7. Selected applications Appendix as discussed by the authors ] is a survey of mixed volumes with bounding boxes and quermass integrals, as well as a discussion of their applications.
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Lp Affine Isoperimetric Inequalities
TL;DR: In this article, the Lp analogues of the Petty projection inequality and the BusemannPetty centroid inequality are established, where the ratio of the functionals is invariant under non-degenerate linear transformations.
Book
Fourier Analysis in Convex Geometry
TL;DR: The Fourier transform and the Busemann-Petty problem have been studied extensively in the literature, see as discussed by the authors for a detailed survey of the Fourier Transform Bibliography Index.