Smooth convex Bodies with proportional projection functions
| dc.creator | Howard, Ralph | |
| dc.creator | Hug, Daniel | |
| dc.date | 2004-08-02 | |
| dc.date.accessioned | 2026-07-07T05:10:57Z | |
| dc.date.available | 2026-07-07T05:10:57Z | |
| dc.description | For a convex body $K\subset\R^n$ and $i\in\{1,...,n-1\}$, the function assigning to any $i$-dimensional subspace $L$ of $\R^n$, the $i$-dimensional volume of the orthogonal projection of $K$ to $L$, is called the $i$-th projection function of $K$. Let $K, K_0\subset \R^n$ be smooth convex bodies of class $C^2_+$, and let $K_0$ be centrally symmetric. Excluding two exceptional cases, that of $(i,j)=(1,n-1)$ and $(i,j)=(n-2,n-1)$, we prove that $K$ and $K_0$ are homothetic if they have two proportional projection functions. The special case when $K_0$ is a Euclidean ball provides an extension of Nakajima's classical three-dimensional characterization of spheres to higher dimensions. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0408028 | |
| dc.identifier | http://arxiv.org/abs/math/0408028 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72087 | |
| dc.subject | Metric Geometry | |
| dc.subject | Differential Geometry | |
| dc.subject | 52A20 | |
| dc.title | Smooth convex Bodies with proportional projection functions | |
| dc.type | text |