If you can hide behind it, can you hide inside it?
| dc.creator | Klain, Daniel A. | |
| dc.date | 2009-05-22 | |
| dc.date.accessioned | 2026-07-07T13:17:35Z | |
| dc.date.available | 2026-07-07T13:17:35Z | |
| dc.description | Let L be a compact convex set in R^n, and let 1 <= d <= n-1. The set L is defined to be d-decomposable if L is a direct Minkowski sum (affine Cartesian product) of two or more convex bodies each of dimension at most d. A compact convex set L is called d-reliable if, whenever each d-dimensional orthogonal projection of L contains a translate of the corresponding d-dimensional projection of a compact convex set K, it must follow that L contains a translate of K. It is shown that, for 1 <= d <= n-1: (1) d-decomposability implies d-reliability. (2) A compact convex set L in R^n is d-reliable if and only if, for all m >= d+2, no m unit normals to regular boundary points of L form the outer unit normals of a (m-1)-dimensional simplex. (3) Smooth convex bodies are not d-reliable. (4) A compact convex set L in R^n is 1-reliable if and only if L is 1-decomposable (i.e. a parallelotope). (5) A centrally symmetric compact convex set L in R^n is 2-reliable if and only if L is 2-decomposable. However, there are non-centered 2-reliable convex bodies that are not 2-decomposable. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/0905.3703 | |
| dc.identifier | http://arxiv.org/abs/0905.3703 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/231157 | |
| dc.subject | Metric Geometry | |
| dc.subject | 52A20 | |
| dc.title | If you can hide behind it, can you hide inside it? | |
| dc.type | text |