Israel Journal of Mathematics

, Volume 152, Issue 1, pp 157–179

Distance sets of well-distributed planar sets for polygonal norms


    • Department of Mechanics and MathematicsMoscow State University
  • Izabella Łaba
    • Department of MathematicsUniversity of British Columbia

DOI: 10.1007/BF02771981

Cite this article as:
Konyagin, S. & Łaba, I. Isr. J. Math. (2006) 152: 157. doi:10.1007/BF02771981


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.

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© The Hebrew University Magnes Press 2006