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We prove that if A is a Borel set in the plane of equal Hausdorff and packing dimension s > 1, then the set of pinned distances {|x − y|… Click to show full abstract
We prove that if A is a Borel set in the plane of equal Hausdorff and packing dimension s > 1, then the set of pinned distances {|x − y| : y ∈ A} has full Hausdorff dimension for all x outside of a set of Hausdorff dimension 1 (in particular, for many x ∈ A). This verifies a strong variant of Falconer’s distance set conjecture for sets of equal Hausdorff and packing dimension, outside the endpoint s = 1.
Keywords:
hausdorff dimension;
dimension;
dimension pinned;
pinned distance
Journal Title: Israel Journal of Mathematics
Year Published: 2019
Link to full text (if available)
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Journal Title: Israel Journal of Mathematics
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!