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


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.


Hausdorff Dimension Geometric Graph Positive Lebesgue Measure Affine Subspace Finite Nonempty Subset 
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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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