# The Role Of The Rogers–Shephard Inequality In The Characterization Of The Difference Body

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### A SHARP ROGERS AND SHEPHARD INEQUALITY FOR THE

by C Bianchini 2008 Cited by 18 We prove a sharp Rogers and Shephard type inequality for the p- difference body of a convex body in the two-dimensional case, for every p

### Claude Ambrose Rogers. 1 November 1920 â ﬂ 5 December

by K Falconer 2015 Cited by 2 Also he explained the importance of being open in sharing mathematics, as body of K. For the following inequality see Rogers and Shephard (30):.

### A Portrayal of Gender and a Description of Gender Roles in

by BB Copenhaver 2002 Cited by 12 Based their gender roles and behavior in their roles, characters faced be afraid to find what is different among what appears to be the same.

### On the Inequality for Volume and Minkowskian Thickness

by G Averkov 2006 Cited by 9 As a simple corollary of the Rogers-Shephard inequality we obtain that (2d difference body of K. It is known that hDK(u) = wK(u). The difference body of

### Near-optimal deterministic algorithms for volume - PNAS

by D Dadush 2013 Cited by 18 An M-ellipsoid E of a convex body K has small covering Rogers Shephard inequality (26); i.e., vol(K − K) ≤ 4nvol(K).

### On Rogers Shephard Type Inequalities for General Measures

by D Alonso-Gutiérrez 2021 Cited by 6 is the characteristic function of a convex body K (Remark 2.10). Rogers Shephard inequality [34], with the main difference of the 38 pages

### The slicing problem by Bourgain - Weizmann Institute of Science

by B Klartag Cited by 2 convex body K ⊆ Rn of volume one, there exists a hyperplane H such that the (n − 1)- the Rogers-Shephard inequality [85].

### Convex Bodies with Minimal Mean Width - umich.edu and

by AA Giannopoulos Cited by 1 The following isotropic characterization of the minimal mean based on the difference body and the Rogers-Shephard inequality [RS] shows.

### ON THE PROBLEM OF REVERSIBILITY OF THE ENTROPY

by SG BOBKOV Cited by 39 Entropy power inequality; convex measure; log-concave; re- verse Brunn-Minkowski inequality; Rogers-Shephard inequality. Sergey G. Bobkov was supported in

### The role of the Rogers-Shephard inequality in the

by J Abardia 2016 Cited by 1 Abstract. The difference body operator enjoys different characterization results relying on its basic properties such as continuity,

### Shadow Boundaries of Convex Bodies - UCL Discovery

Almost all shadow boundaries are sharp (Ewald, Larman and Rogers [11] and Zalgaller. [8]):. Lemma 1.2.1. For every convex body C and every pair of integers

### Asymptotic Convex Geometry - E-class

by AA Giannopoulos Cited by 34 for a discussion on different positions of convex bodies). based on the Rogers-Shephard inequality [125] shows that the symmetry of K

### A Sharp Rogers and Shephard Inequality for the p-Difference

by C Bianchini 2008 Cited by 18 We prove a sharp Rogers and Shephard type inequality for the p difference body of a convex body in the two-dimensional case, for every p > 1

### XVIII EARCO 2018 XVIII Encuentros de Análisis Real y

19 May 2018 Rogers-Shephard inequalities for log-concave functions n, an upper bound for the volume of the difference body K −K in terms of the

### Orlicz centroid bodies - NYU

by E Lutwak Cited by 210 centroid inequality that, for bodies that are not origin-symmetric, are More generally, from the definition of the support function it follows.

### A Brunn-Minkowski Inequality for the Integer Lattice - Western

by RJ Gardner 2001 Cited by 78 A Rogers-Shephard type inequality for the lattice upper bound for the volume of the difference body of a convex body, for the lattice.

### Notes on Schneider's stability estimates for convex sets

by G Toth 2013 Cited by 6 tion ρ : B × B → R defined on the family of all convex bodies B in En For the reverse inequality, assume that in the definition of dD

### On log-concave functions

by A Colesanti 2015 Cited by 12 Functional forms of Blaschke-Santaló and Rogers-Shephard inequalities The characteristic function of a convex body K (compact.

### VOLUME INEQUALITIES FOR SUBSPACES OF Lp Erwin

by E Lutwak 2004 Cited by 144 in dimensions greater than two: the Rogers Shephard difference-body inequality Lieb inequality has had a profound impact on convex geometric analysis.

### FURTHER INEQUALITIES FOR THE (GENERALIZED) WILLS

by D ALONSO-GUTIÉRREZ Cited by 1 Wills functional, intrinsic volumes, log-concave functions, pro- jection function, Asplund product, Brunn-Minkowski type inequalities, Rogers-Shephard.

### The volume of separable states is super-doubly-exponentially

by S Szarek Cited by 1 Since it is conceivable that the inequalities (2) may be of symmetrizations, we use a 1958 result of Rogers and Shephard (see Appendix.

### On Rogers Shephard Type Inequalities for General Measures

by D Alonso Gutiérrez 2019 Cited by 6 is the characteristic function of a convex body K (Remark 2.10). Rogers Shephard inequality [34], with the main difference of the application of.38 pages

### Bounding the Norm of a Log-Concave Vector Via Thin-Shell

by R Eldan 2014 Cited by 14 different argument we establish a similar inequality relying on the thin- the isotropic constant of an isotropic convex body.

### THE MINIMAL VOLUME OF SIMPLICES CONTAINING A

by DE Galicer 2019 Cited by 2 where D(K) stands for the difference body K − K. Note that Equation (5) is a direct By the Rogers-Shephard inequality [AAGM15, Theorem 1.5.2] the cen-.

### Midwest Geometry Conference MGC 2019 - Pablo Stinga

sophisticated microlocal analysis used in earlier proofs by body, which allows us to extend the Rogers-Shephard inequality the product measure.

### Valuations in the Affine Geometry of Convex Bodies - Institute

by M Ludwig Cited by 19 characterization theorem implies that every continuous, equi-affine invariant inequality for difference bodies is the Rogers-Shephard inequality [77].

### Mathematisches Forschungsinstitut Oberwolfach Convex

Eugenia Saorın Gómez (joint with J. Abardia). The role of the Rogers-Shephard inequality in the classification of the difference body

### arXiv:1112.4757v2 [math.FA] 11 Feb 2013 - idUS

by D Alonso Gutiérrez 2013 Cited by 15 definition of θ-convolution of convex bodies, is studied to obtain exten- In [24], Rogers and Shephard obtained the inequality. (1.6). K − K ≤ (.

### CONCENTRATION INEQUALITIES AND - MIMUW

by O Guédon Cited by 34 centration inequalities in the geometry of convex bodies, going from the proof of Dvore- On the way, we meet different topics of functional analysis,

### University of Alberta Some Inequalities in Convex - ERA

by S Taschuk 2013 Cited by 1 these inequalities is implicit in the work of Rogers and Shephard.) Since convex body K, the Minkowski functional, or gauge function,.

### ON SOME GEOMETRIC AND FUNCTIONAL INEQUALITIES

by MA Roysdon 2020 1.3.2 Understanding s-concave functions with convex bodies 23 In the sense of the Rogers-Shephard inequality, the difference body

### CONVEX POLYTOPES

by B GRUNBAUM Cited by 113 C. A. Rogers and G. C. Shephard. [1] The difference body of a convex body , /. London Math. Soc, 33 (1958), 270-

### Rogers and Shephard inequality for the Orlicz difference body

by F Chen 2015 Cited by 3 important role in convex geometry. In this paper, the Rogers and Shephard in- equality for the Orlicz difference body of a convex body in 11 pages

### Distribution of mass in high-dimensional convex bodies - Real

by D Alonso-Gutiérrez 2017 It is clear from the definition that if K is an isotropic convex body then, ∫ proved the following extension of Rogers-Shephard inequality (7),

### The role of the Rogers Shephard inequality in - De Gruyter

by J Abardia-Evéquoz 2017 Cited by 5 The characterization of the difference body operator obtained from this result is as follows: If a map from the compact convex sets to the o-

### FU Robert Thijs Kozma New Density Bounds and Optimal Ball

The role of the Rogers-Shephard inequality in the characterization of the difference body. The difference body of a convex body is defined as the Minkowski

### Relating Brunn-Minkowski and Rogers-Shephard inequalities

and the Rogers-Shephard inequalities in terms of the Minkowski asymmetry Minkowski sum of convex bodies K and C, i.e. K + L = {a + b a ∈ K, b ∈ L}.

### Reversals of Rényi Entropy Inequalities under Log-Concavity

by J Melbourne 2020 Cited by 3 the usual Shannon entropy. Additionally we investigate the entropic Rogers-Shephard inequality studied by Madiman and Kontoyannis,

### Inequalities for dual quermassintegrals of the radial pth mean

by W Wang 2014 Cited by 8 Zhang projection inequality and the Rogers-Shephard inequality, respectively. 2.1 Support function, difference body and projection body.

### On Godbersen's Conjecture - School of Mathematical

by S Artstein-Avidan Cited by 17 This inequality was proved by Rogers and Shephard in [11], A conjectured strengthening of the difference body inequality was suggested in.

### Simplices

leads, with integration tricks, to the Rogers-Shephard inequality. to variants of the difference body inequality appear in applications.

### ROGERS AND SHEPHARD INEQUALITY FOR THE - JSTOR

by F CHEN 2015 Cited by 3 important role in convex geometry. In this paper, the Rogers and Shephard in equality for the Orlicz difference body of a convex body in the

### Algorithms for the Densest Sub-Lattice Problem

by D Dadush 2013 Cited by 14 convex body if it is full-dimensional, compact and convex. Lastly, we will need the classical Rogers-Shephard. [RS57] inequality: Theorem 4.5.

### On the covering index of convex bodies - University of Calgary

by K Bezdek Cited by 7 Covering a convex body by its homothets is a classical notion in discrete geom- By the Rogers-Shephard inequality, we have vol (K − λK).

### Master's Thesis - Makkuva Ashok Vardhan

by AV MAKKUVA 3.2 On sharpness of the doubling-difference entropy inequality 20 A classical result of Rogers and Shephard [20] states that for any convex.

### Functional inequalities related to the Rogers-Shephard

by A Colesanti Cited by 26 of difference function for α-concave functions, with α < 0. The validity of Rogers-Shephard inequality is restricted to convex bodies,

### ROGERS-SHEPHARD AND LOCAL LOOMIS-WHITNEY TYPE

by D Alonso Gutiérrez 2019 Cited by 26 Replacing f and g by the characteristic functions of the two convex bodies above, the inequality. (9) is recovered. The functional counterpart of inequality (10) 40 pages

### Algorithms for the Densest Sub-Lattice Problem

by D Dadush 2013 Cited by 14 convex body K is also a classical problem in mathematics. Lastly, we will need the classical Rogers-Shephard. [RS57] inequality: Theorem 4.5. Let K ⊆ R.

### Concentration of mass on convex bodies

by G Paouris Cited by 241 We establish a sharp concentration of mass inequality for isotropic convex [35] C. A. Rogers and G. C. Shephard, The difference body of a convex body,

### Affine inequalities and radial mean bodies - CiteSeerX

by RJ Gardner 1998 Cited by 115 linking the difference body of K and the polar projection body of K, 1, this becomes the Rogers-Shephard inequality, and when p ! ,1 and