Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772267 | Journal of Functional Analysis | 2017 | 13 Pages |
Abstract
Let K be a convex body in Rn whose centroid is at the origin, let EâG(n,k) be a subspace, and let ξâSnâ1. We find the best constant c=(kn+1)k so that |(K|E)â©Î¾+|kâ¥c|K|E|k, and completely determine the minimizer. Here, |â
|k is k-dimensional volume, K|E is the projection of K onto E, and ξ+={xâRn:ãx,ξãâ¥0}. Our result generalizes both Grünbaum's inequality, and an old inequality of Minkowski and Radon.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
M. Stephen, N. Zhang,