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Israel Journal of Mathematics

, Volume 152, Issue 1, pp 157–179 | Cite as

Distance sets of well-distributed planar sets for polygonal norms

  • Sergei Konyagin
  • Izabella Łaba
Article

Abstract

LetX be a two-dimensional 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 well-distributed set whose distance set Δ satisfies the estimate |Δ∩[0,N]|≤CN 3/2-ε. We also give a necessary and sufficient condition for the existence of a well-distributed set with |Δ∩[0,N]|≤CN.

Keywords

Hausdorff Dimension Geometric Graph Positive Lebesgue Measure Affine Subspace Finite Nonempty Subset 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© The Hebrew University Magnes Press 2006

Authors and Affiliations

  1. 1.Department of Mechanics and MathematicsMoscow State UniversityMoscowRussia
  2. 2.Department of MathematicsUniversity of British ColumbiaVancouverCanada

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