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Distance sets of welldistributed planar sets for polygonal norms
 Sergei Konyagin,
 Izabella Łaba
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LetX be a twodimensional normed space, and letBX be the unit ball inX. We discuss the question of how large the set of extremal points ofBX may be ifX contains a welldistributed set whose distance set Δ satisfies the estimate Δ∩[0,N]≤CN ^{3/2ε}. We also give a necessary and sufficient condition for the existence of a welldistributed set with Δ∩[0,N]≤CN.
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 Title
 Distance sets of welldistributed planar sets for polygonal norms
 Journal

Israel Journal of Mathematics
Volume 152, Issue 1 , pp 157179
 Cover Date
 20061201
 DOI
 10.1007/BF02771981
 Print ISSN
 00212172
 Online ISSN
 15658511
 Publisher
 SpringerVerlag
 Additional Links
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 Industry Sectors
 Authors

 Sergei Konyagin ^{(1)}
 Izabella Łaba ^{(2)}
 Author Affiliations

 1. Department of Mechanics and Mathematics, Moscow State University, 119992, Moscow, Russia
 2. Department of Mathematics, University of British Columbia, V6T 1Z2, Vancouver, B.C., Canada