On a planar variant of the Kakeya problem
| dc.creator | Rogers, Keith M. | |
| dc.date | 2005-02-16 | |
| dc.date | 2005-11-29 | |
| dc.date.accessioned | 2026-07-07T06:39:27Z | |
| dc.date.available | 2026-07-07T06:39:27Z | |
| dc.description | A K^n_2-set is a set of zero Lebesgue measure containing a translate of every plane in an (n-2)-dimensional manifold in Gr(n,2), where the manifold fulfills a curvature condition. We show that this is a natural class of sets with respect to the Kakeya problem and prove that dim_H(E)\ge 7/2 for all K^4_2-sets E. When the underlying field is replaced by the complex numbers C, we get dim_H(E)\ge 7 for all K^4_2-sets over C, and we construct an example to show that this is sharp. Thus K^4_2-sets over C do not necessarily have full Hausdorff dimension. | |
| dc.description | 14 pages, to appear, Math. Res. Lett. Includes a mathematical correction, and changes to the acknowledgements | |
| dc.identifier | https://arxiv.org/abs/math/0502360 | |
| dc.identifier | http://arxiv.org/abs/math/0502360 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101083 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 42B10; 28A75 | |
| dc.title | On a planar variant of the Kakeya problem | |
| dc.type | text |