Universität zu Köln

de Oliveira Filho, Fernando Mario and Vallentin, Frank ORCID: 0000-0002-3205-4607 (2019). A COUNTEREXAMPLE TO A CONJECTURE OF LARMAN AND ROGERS ON SETS AVOIDING DISTANCE 1. Mathematika, 65 (3). S. 785 - 788. LONDON: LONDON MATH SOC. ISSN 2041-7942

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Abstract

For each n >= 2 we construct a measurable subset of the unit ball in 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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code de Oliveira Filho, Fernando Mario UNSPECIFIED UNSPECIFIED UNSPECIFIED Vallentin, Frank UNSPECIFIED orcid.org/0000-0002-3205-4607 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-138989
DOI:	10.1112/S0025579319000160
Journal or Publication Title:	Mathematika
Volume:	65
Number:	3
Page Range:	S. 785 - 788
Date:	2019
Publisher:	LONDON MATH SOC
Place of Publication:	LONDON
ISSN:	2041-7942
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language Mathematics, Applied; Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/13898