On the Distance Sets of Self-Similar Sets

Abstract

We show that if K is a self-similar set in the plane with positive length, then the distance set of K has Hausdorff dimension one.

13 pages, one figure; exposition clarified and typos corrected in v2; to appear in Nonlinearity

References in corpus (2)

• Some connections between Falconer's distance set conjecture, and sets of Furstenburg type
• On the Erdos distinct distance problem in the plane