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A COUNTEREXAMPLE TO A CONJECTURE OF LARMAN AND ROGERS ON SETS AVOIDING DISTANCE 1
Published online by Cambridge University Press: 14 May 2019
Abstract
For each $n\geqslant 2$ 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 unit ball. This disproves a conjecture of Larman and Rogers from 1972.
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- Research Article
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- Copyright © University College London 2019
Footnotes
The second author was partially supported by the SFB/TRR 191 “Symplectic Structures in Geometry, Algebra and Dynamics”, funded by the DFG, and the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie agreement number 764759.
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