A counterexample to a conjecture of Larman and Rogers on sets avoiding distance 1

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Abstract

For each (Formula presented.) we construct a measurable subset of the unit ball in (Formula presented.) that does not contain pairs of points at distance 1 and whose volume is greater than (Formula presented.) times the volume of the unit ball. This disproves a conjecture of Larman and Rogers from 1972.

Original languageEnglish
Pages (from-to)785-787
Number of pages3
JournalMathematika
Volume65
Issue number3
DOIs
Publication statusPublished - 2019

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