On the blaschke-santal ́o inequality
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 WebAsharp upper boundforthe volume product is givenby the Blaschke-Santal´o Inequality. Theorem (TheBlaschke-Santal´oInequality). Let Bdenote the Euclidean unit ball of R N. …
On the blaschke-santal ́o inequality
Did you know?
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 … 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 …
WebSemantic 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 ... Webintroduced notions, the equality conditions of the sine Blaschke-Santal´o inequality are settled. 2024 Mathematics Subject Classification: 52A20, 52A30, 52A40, 94A15. 1 Introduction
http://www.math.u-szeged.hu/~vigvik/preprints/hyperconv.pdf
WebBlaschke{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 ...
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, … high speed photography ielts reading answersWeb28 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. how many days left till schoolWebSome 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 how many days left till school endsWeb15 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 … how many days left till september 14Web1 de jan. de 2009 · Abstract. We give a simple proof of a functional version of the Blaschke–Santaló inequality due to Artstein, Klartag and Milman. The proof is by induction on the dimension and does not use the Blaschke–Santaló inequality. To cite this article: J. Lehec, C. R. Acad. Sci. Paris, Ser. I 347 (2009). high speed photography powder on a speakerWeb15 de set. de 2024 · This paper is dedicated to study the sine version of polar bodies and establish the L p-sine Blaschke-Santaló inequality for the L p-sine centroid body. The L … how many days left till ramadan ends 2022Web4 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 … how many days left till new year