| dc.rights.license | https://creativecommons.org/licenses/by-sa/2.5/ar/ | es_AR |
| dc.contributor.author | Shmerkin, Pablo | es_AR |
| dc.contributor.author | Yavicoli, Alexia | es_AR |
| dc.date.accessioned | 2023-12-21T16:34:40Z | |
| dc.date.available | 2023-12-21T16:34:40Z | |
| dc.date.issued | 2023 | |
| dc.identifier.uri | https://repositorio.utdt.edu/handle/20.500.13098/12235 | |
| dc.description.abstract | We prove that for 1 ≤ k < d, if E is a Borel subset of Rd of Hausdorff
dimension strictly larger than k, the set of (k+1)-volumes determined by k+2 points
in E has positive one-dimensional Lebesgue measure. In the case k = d−1, we obtain
an essentially sharp lower bound on the dimension of the set of tuples in E generating
a given volume. We also establish a finer version of the classical slicing theorem of
Marstrand-Mattila in terms of dimension functions, and use it to extend our results
to sets of “dimension logarithmically larger than k”. | es_AR |
| dc.format.extent | 12 p. | es_AR |
| dc.format.medium | application/pdf | es_AR |
| dc.language | eng | es_AR |
| dc.publisher | Universidad Torcuato Di Tella | es_AR |
| dc.rights | info:eu-repo/semantics/openAccess | es_AR |
| dc.subject | Mathematics | es_AR |
| dc.subject | theorems | es_AR |
| dc.title | On the volumes of simplices determined by a subset of Rd | es_AR |
| dc.type | info:eu-repo/semantics/preprint | es_AR |
| dc.subject.keyword | theorem of Marstrand-Mattila | es_AR |
| dc.subject.keyword | Hausdorff dimension | es_AR |
| dc.subject.keyword | Dimension functions | es_AR |
| dc.subject.keyword | Dimension logarithmically larger than k | es_AR |
| dc.subject.keyword | Slicing theorem | es_AR |
| dc.type.version | info:eu-repo/semantics/submittedVersion | es_AR |
