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
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