On a Problem Related to Sphere and Circle Packing | Zendy

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On a Problem Related to Sphere and Circle Packing

Author(s) -

Mitsis T.

Publication year - 1999

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/s0024610799007838

Subject(s) - hausdorff dimension , mathematics , packing dimension , hausdorff measure , set (abstract data type) , dimension (graph theory) , lebesgue measure , hausdorff space , hausdorff distance , combinatorics , spheres , measure (data warehouse) , lebesgue integration , minkowski–bouligand dimension , pure mathematics , mathematical analysis , computer science , fractal dimension , fractal , physics , astronomy , database , programming language

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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