On the blaschke-santal ́o inequality

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August undefined, 2024

WebOn the Blaschke-Santal6 inequality By MATHIEU MEYER and ALAIN PAJOR 1. Introduction. Let K be a convex body in the n-dimensional Euclidean space E (= En). For z in int (K), the interior of K, let K z be the polar body of K with respect to z; denoting by (,) the scalar product, we have: Webevery convex body with bounded isotropic constant satisﬁes the reverse Santal´o inequality, and then that all bodies do. We ﬁrst recall the statements and the history of the results.

Some functional forms of Blaschke–Santaló inequality - Springer

WebOriginal language: English (US) Pages (from-to) 106-112: Number of pages: 7: Journal: Annals of the New York Academy of Sciences: Volume: 440: Issue number: 1: DOIs Webintroduced notions, the equality conditions of the sine Blaschke-Santal´o inequality are settled. 2024 Mathematics Subject Classification: 52A20, 52A30, 52A40, 94A15. 1 Introduction northborough excise tax

On a generalised Blaschke-Santal\`o inequality - Semantic Scholar

Web23 de set. de 2013 · A complete 3-dimensional Blaschke-Santal ... The proof of Proposition 4.2 shows that it would be desirable to extend inequality (4.1) to higher dimensions. WebStudia Math. 88, 68–84 (1988). W. Blaschke, Vorlesungen über Differentialgeometrie II. Berlin-Heidelberg-New York 1923. J. Bourgain and V. D. Milman, New volume ratio … WebHenry M. Paulson, Jr. served under President George W. Bush as the 74th Secretary of the Treasury from June 2006 until January 2009. Before coming to Treasury, Paulson was … northborough drive

On the Blaschke-Santaló inequality - University of Paris-Est …

A sharp Blaschke{Santal o inequality for -concave functions

Web20 de set. de 2006 · We establish new functional versions of the Blaschke-Santaló inequality on the volume product of a convex body which generalize to the non … Web26 de mar. de 2024 · The Blaschke–Santaló inequality was proven by W. Blaschke in 1917, for $ n = 2,3 $, and by L. Santaló in 1949, for all $ n \geq 2 $. Both proofs use the … how to replace wipers bladesWeb19 de dez. de 2006 · We establish new functional versions of the Blaschke–Santaló inequality on the volume product of a convex body which generalize to the non … northborough drive houston tx

"Web28 de mar. de 2024 · Key words and phr ases: Moment–Entropy inequalities, Blaschke–Santal´ o inequality, ... (1.1) contain an important extension of the Blaschk e-Santal´ o inequality (one of the. " - On the blaschke-santal ́o inequality

On the blaschke-santal ́o inequality

(PDF) A complete 3-dimensional Blaschke-Santaló diagram

WebGlances at the Insane in Other Lands: V.-The New Brunswick Asylum, St. John. Web1 de dez. de 2013 · The Blaschke-Santal\'o Inequality is the assertion that the volume product of a centrally symmetric convex body in Euclidean space is maximized by (and …

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WebObserve that it follows from the Blaschke-Santal´o inequality that the Santalo-point x 0 ∈ S(K,1) and that S(K,1) = {x 0} if and only if K is an ellipsoid. Thus S(K,t) has non-empty interior for some t<1 if and only if K is not an ellipsoid. In the ﬁrst part of this paper we show some properties of S(K,t) and give

WebKeywords Blaschke-Santalo inequality convexity -concavity log-concavity Mathematics Subject Classi cation (2010) 52A40 26B25 1 Blaschke{Santal o type inequalities We begin by recalling the classic Blaschke-Santal o inequality. A convex body in Rn is compact, convex set with non-empty interior. Such a convex body Kis called symmetric if K= K. Web15 de jan. de 2024 · More specifically, our work concerns the Blaschke-Santaló inequality for convex sets and some functional versions of it. The Blaschke-Santaló inequality is …

WebOn the Blaschke-Santal6 inequality By MATHIEU MEYER and ALAIN PAJOR 1. Introduction. Let K be a convex body in the n-dimensional Euclidean space E (= En). For … http://www.math.u-szeged.hu/~vigvik/preprints/hyperconv.pdf

WebSome functional forms of Blaschke–Santaló inequality 381 Theorem Let ρ: R+ → R+ be a log-concave non-increasing function and let φ be a convex function such that 0 < Rn ρ(φ(x))dx < +∞.Then for some z ∈ Rn, one has R n ρ(φ(x))dx R ρ(Lzφ(y))dy ≤ Rn ρ x 2 2 dx 2. In all these functional forms of Blaschke–Santaló inequality, we determine the

WebOn the Blaschke-Santal6 inequality By MATHIEU MEYER and ALAIN PAJOR 1. Introduction. Let K be a convex body in the n-dimensional Euclidean space E (= En). For … northborough emsWebAs a seminal inequality for log-concave functions, we rst mention the celebrated Pr ekopa{Leindler inequality which is universally recognized as the functional form of the … northborough election resultsWebOne is the stability version of the Blaschke-Santaló inequality, and the other is a stability version of the Prékopa-Leindler inequality for even functions in higher dimensions, where a recent ... how to replace wooden fence postWeb4 de ago. de 2014 · The Blaschke-Santal\'o Inequality is the assertion that the volume product of a centrally symmetric convex body in Euclidean space is maximized by (and … northborough eye centerWeb7 de ago. de 2024 · In this paper, we establish a generalised Blaschke-Santalò inequality for convex bodies in . This inequality gives an upper bound estimate for the product of … northborough eventsWeb11 de mai. de 2024 · The first known case of a conviction for blasphemy in Ireland was in 1328, when a man named Adam Duff O'Toole branded Christian scripture as a fable and … northborough dental officesWebbecause Blaschke-Santal´o inequality can be applied to K∗G(K). But if K is centrally symmetric, the situation is simpler: minz K∗z is reached at 0, and then K · K ≤ Bn 2 2. We shall also make use of the equality case in Blaschke-Santal´o inequality: there is equality if and only if Kis an ellipsoid. At the end northborough dog grooming