On the distance sets of Ahlfors-David regular sets

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Orponen , T 2017 , ' On the distance sets of Ahlfors-David regular sets ' , Advances in Mathematics , vol. 307 , pp. 1029-1045 . https://doi.org/10.1016/j.aim.2016.11.035

Title: On the distance sets of Ahlfors-David regular sets
Author: Orponen, Tuomas
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2017-02-05
Language: eng
Number of pages: 17
Belongs to series: Advances in Mathematics
ISSN: 0001-8708
URI: http://hdl.handle.net/10138/313040
Abstract: prove that if empty set not equal K subset of R-2 is a compact s-Ahlfors-David regular set with s >= 1, then dim(p) D(K) = 1, where D(K) := {vertical bar x - y vertical bar : x, y is an element of K} is the distance set of K, and dime stands for packing dimension. The same proof strategy applies to other problems of similar nature. For instance, one can show that if empty set not equal K subset of R-2 is a compact s-Ahlfors David regular set with s >= 1, then there exists a point x(0) is an element of K such that dime K . (K - x(0)) = 1. (C) 2016 Elsevier Inc. All rights reserved.
Subject: Distance sets
Packing dimension
Entropy
111 Mathematics
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