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