On the distance sets of Ahlfors-David regular sets

Visa fullständig post



Permalänk

http://hdl.handle.net/10138/313040

Citation

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

Titel: On the distance sets of Ahlfors-David regular sets
Författare: Orponen, Tuomas
Upphovmannens organisation: Department of Mathematics and Statistics
Datum: 2017-02-05
Språk: eng
Sidantal: 17
Tillhör serie: Advances in Mathematics
ISSN: 0001-8708
DOI: https://doi.org/10.1016/j.aim.2016.11.035
Permanenta länken (URI): http://hdl.handle.net/10138/313040
Abstrakt: 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
Referentgranskad: Ja
Licens: cc_by_nc_nd
Användningsbegränsning: openAccess
Parallelpublicerad version: acceptedVersion


Filer under denna titel

Totalt antal nerladdningar: Laddar...

Filer Storlek Format Granska
1509.06675.pdf 179.8Kb PDF Granska/Öppna

Detta dokument registreras i samling:

Visa fullständig post