On a Problem in Geometric Measure Theory Related to Sphere and Circle Packing

Author: Mitsis, Themistoklis

Year: 1998

Degree: Dissertation (Ph.D.)

Advisor: Wolff, Thomas H.

Committee Members: Wolff, Thomas H.; Kahn, Jeremy; Kechris, Alexander S.; Last, Y.

Option: Mathematics

DOI: 10.7907/992h-9263

Abstract

In this thesis we prove that a Borel set which contains spheres centered at all points of a Borel set of Hausdorff dimension greater than 1 must have positive Lebesgue measure, and, using the same method, we rederive a special case of Stein's spherical means maximal inequality. We also prove the corresponding result for circles, provided that the set of centers has Hausdorff dimension greater than 3/2.

Files

• Mitsis_T_1998.pdf (application/pdf)