The width-volume inequality
| dc.creator | Guth, Larry | |
| dc.date | 2006-09-20 | |
| dc.date.accessioned | 2026-07-07T07:25:01Z | |
| dc.date.available | 2026-07-07T07:25:01Z | |
| dc.description | We prove that a bounded open set U in Euclidean n-space has k-width less than C(n) Volume(U)^{k/n}. Using this estimate, we give lower bounds for the k-dilation of degree 1 maps between certain domains in Euclidean space. In particular, we estimate the smallest (n-1)-dilation of any degree 1 map between two n-dimensional rectangles. For any pair of rectangles, our estimate is accurate up to a dimensional constant C(n). We give examples in which the (n-1)-dilation of the linear map is bigger than the optimal value by an arbitrarily large factor. | |
| dc.description | 31 pages, 4 figures, to be published in Geometric and Functional Analysis | |
| dc.identifier | https://arxiv.org/abs/math/0609569 | |
| dc.identifier | http://arxiv.org/abs/math/0609569 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116588 | |
| dc.subject | Differential Geometry | |
| dc.subject | Metric Geometry | |
| dc.subject | 53C99 | |
| dc.title | The width-volume inequality | |
| dc.type | text |