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Fenchel's inequality

WebOct 2, 2024 · Various Alexandrov-Fenchel type inequalities have appeared and played important roles in convex geometry, matrix theory and complex algebraic geometry. It has been noticed for some time that they share some striking analogies and have intimate relationships. The purpose of this article is to shed new light on this by comparatively … WebMar 13, 2024 · $\begingroup$ Many thanks and I'm sorry @Zim , I know the article as the preprint from arXiv with identificator 0710.2307 that you can search (or searching for the title of the article) in the browser of arXiv. I would like to know if it is possible to state a similar Lemma 2.1 of [1] for Fenchel–Legendre transforms, in the spirit of the inequality of my …

[2011.04059] The Extremals of the Alexandrov-Fenchel Inequality …

WebFenchel inequality follows from the Brunn-Minkowski inequality. We do not provide here an alternative proof for the Alexandrov-Fenchel inequality in two dimensions. Thus, … Websame shape. It follows from the Legendre-Fenchel inequality, a family of non-metric distances BF,F∗(x,y) = F(x) + F∗(y) − xTy≥ 0 ∀x∈ X,y∈ Y that plays the role of canonical divergences of flat spaces in information geometry. Properties of the Legendre transformation are finally briefly listed. pension regulation for the army 1961 https://sh-rambotech.com

A stability estimate for the Aleksandrov–Fenchel inequality under ...

WebIn mathematics and mathematical optimization, the convex conjugate of a function is a generalization of the Legendre transformation which applies to non-convex functions. It is … Webversion of the Alexandrov-Fenchel inequality for mixed discriminants and a determinantal generalization of various Alexandrov-Fenchel type inequalities. 1. Introduction One of the most fundamental results in convex geometry is the Alexandrov-Fenchel (AF for short) inequality for mixed volumes on convex bodies in the Euclidean spaces. There are at WebThe Fenchel conjugate of a function f : S → R is defined as f?(θ) = sup w∈S hw,θi−f(w) . If f is closed and convex then the Fenchel conjugate of f? is f itself. The Fenchel-Young inequality states that for any w and θ we have that f(w) + … pension regulator scam pledge

One more proof of the Alexandrov–Fenchel inequality

Category:One more proof of the Alexandrov-Fenchel inequality

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Fenchel's inequality

A stability estimate for the Aleksandrov–Fenchel inequality under ...

Webby the Fenchel-Young Inequality. If E is subdi erentiable at E, let q 2@E(u). We readily obtain E (u) = sup p hp;ui E (p) hq;ui E (q) = E(u); by the equality of the Fenchel-Young … http://staff.ustc.edu.cn/~yongwei/folder/AW_ICCM2024.pdf

Fenchel's inequality

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WebGaussian isoperimetric inequalities I Recall the relation between the Brunn-Minkowski inequalities and the u-niqueness of area measures. (Aleksandrov 1930s) I Di erentiate the Gaussian Brunn-Minkowski inequality? I Di erentiating each inequality, one can obtain a Minkowski type inequality Z Sn 1 (h L h K)dS n;K n(K)log n(L) n(K); with equality ... WebThe Aleksandrov-Fenchel inequalities ([1], [2]) for the quermassintegrals for convex domains are fundamental inequalities in classical geometry. For a bounded smooth, convex domain A ⊂ Rn+1, and B the unit ball in Rn+1, Minkowski considered the volume expansion of the set A+tB with the expansion Vol(A+tB)= n+1 k=0 V n+1−k(A)t k (1) Thus ...

WebMar 14, 2024 · Download PDF Abstract: In this article, we will use the harmonic mean curvature flow to prove a new class of Alexandrov-Fenchel type inequalities for strictly convex hypersurfaces in hyperbolic space in terms of total curvature, which is the integral of Gaussian curvature on the hypersurface. We will also use the harmonic mean curvature … Webinequalities for mixed volumes Aleksandrov-Fenchel inequality(4.1) Isoperimetric for Kn Brascamp-Lieb inequal-ity (2.6) Brunn-Minkowski for mixed volumes (4.2) Figure 1.1: A part of the vast web of inequalities related to the Brunn-Minkowski inequal-ity. In chapter3the study of mixed volumes is presented and the fundamental prop-

WebNov 8, 2024 · The Alexandrov-Fenchel inequality, a far-reaching generalization of the classical isoperimetric inequality to arbitrary mixed volumes, lies at the heart of convex geometry. The characterization of its extremal bodies is a long-standing open problem that dates back to Alexandrov's original 1937 paper. The known extremals already form a … WebFeb 3, 2024 · We show that the iterates generated by a generic first-order meta-algorithm satisfy a canonical perturbed Fenchel duality inequality. The latter in turn readily yields …

WebSep 1, 2024 · The Bochner method was already used in [20] to provide new proofs of the Alexandrov-Fenchel inequality, a much deeper result of which (1.6) is a special case, and of the Alexandrov mixed ...

http://staff.ustc.edu.cn/~yongwei/folder/AW_ICCM2024.pdf pension release over 55pension regulator webinarWebFeb 18, 2024 · New dynamic Hilbert-type inequalities in two independent variables involving Fenchel–Legendre transform. A. El-Deeb, S. Rashid, Z. Khan, S. Makharesh. Mathematics. 2024. In this paper, we establish some dynamic Hilbert-type inequalities in two independent variables on time scales by using the Fenchel–Legendre transform. pension release under 55 ukWebIn particular, the de nition of f yields the following (Young-Fenchel inequality) f(x) xy f(y); (6.2) where the last inequality holds for any y. Using the notion of convex conjugate, we obtain a variational representation of f-divergence in ... Note: The inequality (6.8) can be interpreted as follows: On the left hand side of the inequality we ... pension releaseWebThe Fenchel family name was found in the USA, the UK, and Scotland between 1861 and 1920. The most Fenchel families were found in USA in 1920. In 1880 there were 7 … pension rehwinkel nalbachhttp://www.stat.yale.edu/~yw562/teaching/598/lec06.pdf today tandartsWebinequality, the so-called Alexandrov-Fenchel inequalities: For smooth convex hypersurface Min Rn+1 enclosing a bounded domain , we de ne the k-th … today tandartsen