# Distance sets of well-distributed planar sets for polygonal norms

Article

- Received:

DOI: 10.1007/BF02771981

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

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## Abstract

Let*X* be a two-dimensional normed space, and let*BX* be the unit ball in*X*. We discuss the question of how large the set of extremal points of*BX* may be if*X* 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*.

## Copyright information

© The Hebrew University Magnes Press 2006