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Journal of the London Mathematical Society 1999 60(2):501-516; doi:10.1112/S0024610799007838
© 1999 by London Mathematical Society
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© The London Mathematical Society

On a Problem Related to Sphere and Circle Packing

T. Mitsis

Nestou 6, Athens 14342, Greece themis{at}cco.caltech.edu, tmitsis{at}yahoo.com

Received 23 April 1998. Revision received 14 July 1998.

The paper proves that a set which contains spheres centered at all points of a set of Hausdorff dimension greater than 1 must have positive Lebesgue measure. It also proves the corresponding result for circles, provided that the set of centers has Hausdorff dimension greater than 3/2.


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