A counterexample to a conjecture of Larman and Rogers on sets avoiding distance 1
| Autor: | Filho, Fernando Mário de Oliveira, Vallentin, Frank |
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| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Mathematika 65 (2019) 785-787 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1112/S0025579319000160 |
| Popis: | For $n \geq 2$ we construct a measurable subset of the unit ball in $\mathbb{R}^n$ that does not contain pairs of points at distance 1 and whose volume is greater than $(1/2)^n$ times the volume of the ball. This disproves a conjecture of Larman and Rogers from 1972. Comment: 3 pages, 1 figure; final version to appear in Mathematika |
| Databáze: | arXiv |
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