Fourier transform and L_p-mixed centroid bodies
نویسندگان
چکیده
منابع مشابه
Orlicz Centroid Bodies
The sharp affine isoperimetric inequality that bounds the volume of the centroid body of a star body (from below) by the volume of the star body itself is the Busemann-Petty centroid inequality. A decade ago, the Lp analogue of the classical BusemannPetty centroid inequality was proved. Here, the definition of the centroid body is extended to an Orlicz centroid body of a star body, and the corr...
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In [F] Firey extended the notion of the Minkowski sum, and introduced, for each real p, a new linear combination of convex bodies, that he called p-sums. Lutwak [Lu2], [Lu3] showed that these Firey sums lead to a Brunn-Minkowski theory for each p ≥ 1. He introduced the notions of p-mixed volume, p-surface area measure, and proved an integral representation and inequalities for p-mixed volumes, ...
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Abstract. The Fourier analytic approach to sections of convex bodies has recently been developed and has led to several results, including a complete analytic solution to the BusemannPetty problem, characterizations of intersection bodies, extremal sections of lp-balls. In this article, we extend this approach to projections of convex bodies and show that the projection counterparts of the resu...
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In [F] Firey extended the notion of the Minkowski sum, and introduced, for each real p, a new linear combination of convex bodies, what he called p-sums. E. Lutwak [Lu2], [Lu3] showed that these Firey sums lead to a Brunn-Minkowski theory for each p ≥ 1. He introduced the notions of p-mixed volume, p-surface area measure, and proved an integral representation and inequalities for p−mixed volume...
متن کاملSections of Star Bodies and the Fourier Transform
A new approach to the study of sections of star bodies, based on methods of Fourier analysis, has recently been developed. The idea is to express certain geometric properties of bodies in terms of the Fourier transform and then apply methods of harmonic analysis to solve geometric problems. This approach has already led to several results including an analytic solution to the Busemann-Petty pro...
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ژورنال
عنوان ژورنال: Journal of Mathematical Inequalities
سال: 2012
ISSN: 1846-579X
DOI: 10.7153/jmi-06-15