On the blaschke-santal ́o inequality
WebThe functional Blaschke-Santalo inequality of log-concave functions is the analogue of Blaschke-Santal´o inequality of convex bodies. Theorem 1.1. (Artstein, Klartag, … 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
On the blaschke-santal ́o inequality
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WebSuch 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. Web11:00-11:20 Dmitry Faifman: A Funk extension of the Blaschke-Santal´o inequality 11:30-11:50 Gil Solanes: Santal´o point for the Holmes-Thompson boundary area 15:30-16:20 Elisabeth Werner: Blaschke-Santal´o inequality for many functions and geodesic barycenters of measures
WebMOMENT-ENTROPY INEQUALITIES 759 Here ωn = πn/2/(1 + n/2) denotes the volume of the unit ball in Rn.If K is an origin-symmetric convex body and L is the polar of K, then the above inequality is the classical Blaschke–Santaló inequality, with sharp constant. See, for example, the books of Gardner (1995), Leichtweiß (1998), Schneider (1993)
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 … WebEnjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube.
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.
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 bismuth antibioticWebAsharp upper boundforthe volume product is givenby the Blaschke-Santal´o Inequality. Theorem (TheBlaschke-Santal´oInequality). Let Bdenote the Euclidean unit ball of R N. … bismuth antimonideWebHenry 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 … darlington roll extricationWebSemantic Scholar extracted view of "Asymmetric Blaschke-Santaló functional inequalities" by J. Haddad et al. Skip to search form Skip to main content Skip to ... {Asymmetric Blaschke-Santal{\'o} functional inequalities}, author={Juli{\'a}n Haddad and Carlos Hugo Jim{\'e}nez and Marcos Montenegro}, journal={Journal of Functional ... darlington road holiday flWebBlaschke{Santal o inequality, leads to an isoperimetric inequality for the product of the volumes of a body and its polar centroid body, called the polar Busemann{Petty centroid inequality. An L p analogue of the latter inequality was established by Lutwak and Zhang [33], who showed that it provides an L p extension of the Blaschke{Santal o ... bismuth antimonyWebwidth 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-Santal´o inequality, intrinsic volume, quermassintegral, polar bismuth antimony phase diagramWeb15 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 … bismuth architecte