Distance sets of well-distributed planar sets for polygonal norms |
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| Authors: | Sergei Konyagin Izabella Łaba |
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| Institution: | (1) Department of Mechanics and Mathematics, Moscow State University, 119992 Moscow, Russia;(2) Department of Mathematics, University of British Columbia, V6T 1Z2 Vancouver, B.C., Canada |
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| 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. |
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