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On maximal Euclidean sets avoiding certain distance configurations

Published online by Cambridge University Press:  24 October 2008

H. T. Croft  and
K. J. Falconer
H. T. Croft
Affiliation:
Peterhouse, Cambridge, and Corpus Christi College, Cambridge
K. J. Falconer
Affiliation:
Peterhouse, Cambridge, and Corpus Christi College, Cambridge
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Extract

Let us say that a set points in a Euclidean space has property (2) if no 2 points X, Y ∈ S have X Y > 1. Then an easy observation is the following:

The maximum area (Lebesgue measure) of a plane set S with property(2) is ¼π, attained only when S is (essentially) a disc.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 1 , January 1981 , pp. 79 - 88
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

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