On the blaschke-santal ́o inequality
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 … Web1 de dez. de 2013 · The Blaschke-Santaló Inequality is the assertion that the volume product of a centrally symmetric convex body in Euclidean space is maximized by (and …
On the blaschke-santal ́o inequality
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Webintroduced notions, the equality conditions of the sine Blaschke-Santal´o inequality are settled. 2024 Mathematics Subject Classification: 52A20, 52A30, 52A40, 94A15. 1 Introduction WebSantal o proved in [23] that for every convex body K, there exists a unique point s 2intKsuch that vol(Ks) vol(Kz) for all z 2intK. This unique point s is called the Santal o point of K. For a convex body K, the quantity vol(K)vol(Ks) is usually called the volume product of K. The Blaschke{Santal o inequality (Blaschke
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: WebEuclidean inequalities, the Urysohn inequality connecting mean width and volume, and the Blaschke-Santal´o inequality for the volumes of polar convex bodies. Two proofs are given; the first one can be adapted to hyperbolic space. MSC 2000: 52A40 (primary); 52A55, 52A22 (secondary) Keywords: spherical convexity, Urysohn inequality, Blaschke-
Web7 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 …
Web4 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 …
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 … sideshow stylistics songWeb1 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 … the play wicked tourWebOne 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 ... the play witWebObserve 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 sideshow symbiote spidermanWebSuch a result is called the Lp-Blaschke-Santal¶o inequality. This name comes from the fact that, when K is origin symmetric and p goes to inflnity, (4) tends to the volume product. We shall deal with the problem of obtaining reverse form of the Lp-Blaschke-Santal¶o inequality and we solve it, for d = 2, by exploiting Theorem 1. the play within the play pleases the nobilityWeb16 de dez. de 2006 · Request PDF On Dec 16, 2006, Erwin Lutwak published On the Blaschke-Santaló inequality Find, read and cite all the research you need on ResearchGate sideshow synopsisWeb26 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 … the play within