WebMar 16, 2024 · This is the first comprehensive monograph to thoroughly investigate constant width bodies, which is a classic area of interest within convex geometry. It examines bodies of constant width from several points of view, and, in doing so, shows surprising connections between various areas of mathematics. Concise explanations and detailed … WebJun 15, 2016 · In this article, we introduce a new concept of general mixed width-integral of convex bodies, and establish some of its inequalities, such as isoperimetric …

Dual Brunn–Minkowski inequality for volume differences

WebSep 22, 2009 · Lutwak E.: Mixed width-integrals of convex bodies. Israel J. Math. 28(3), 249–253 (1977) ... Mercer, A.M.: Extensions of Popoviciu’s inequality using a general method. J. Ineq. Pure Appl. Math. 4 Article 11, 4 pp (2003) Google Scholar Schneider R.: Convex Bodies: The Brunn–Minkowski Theory. Cambridge University Press, New York … WebAbstract: General mixed width-integral of convex bodies is introduced. We prove some important inequalities, such as, isoperimetric inequali-ty, Aleksandrov-Fenchel inequality … flash drive and hard drive

Czechoslovak Mathematical Journal

WebA general result for a convex body K and a convex increasing real valued function gives inequalities for sets of constant width and sets with equichordal points as special cases. Preliminaries By a convex body in Rn , n > 2, we mean a compact convex subset of Rn with nonempty interior. All convex bodies are assumed to contain the origin WebFeb 18, 2024 · A smooth convex body is a convex body whose boundary is a smooth hypersurface. The global convexity (in the sense of Definition 5.2.1) is equivalent to the non-negativity of the curvature (extrinsic or intrinsic), see [10, 12]. A general convex body is neither polyhedral nor smooth. Take for example a Cantor set in the circle and form its ... http://www.iaeng.org/IJAM/issues_v50/issue_1/IJAM_50_1_23.pdf check curtains asda