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- W1540694146 abstract "In this paper we prove two new inequalities about width- integrals of centroid and projection bodies. Two analogs of the dual Brunn- Minkowski inequality for width-integral of convex bodies are established. 0. Definitions and preliminary results The setting for this paper is n-dimensional Euclidean space R n (n > 2). Let K n denote the set of convex bodies (compact, convex subsets with non-empty interi- ors) in R n . Let ' n denote the set of star bodies in R n . The subset of ' n consisting of the centred star bodies will be denoted by ' n. We reserve the letter u for unit vectors, and the letter B is reserved for the unit ball centered at the origin. The surface of B is S n 1 . For u 2 S n 1 , let Eu denote the hyperplane, through the origin, that is orthogonal to u. We will use K u to denote the image of K under an orthogonal projection onto the hyperplane Eu." @default.
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- W1540694146 date "2007-01-01" @default.
- W1540694146 modified "2023-10-16" @default.
- W1540694146 title "ON ANALOGS OF THE DUAL BRUNN-MINKOWSKI INEQUALITY FOR WIDTH-INTEGRALS OF CONVEX BODIES" @default.
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