, Volume 152, Issue 1, pp 157-179

Distance sets of well-distributed planar sets for polygonal norms

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

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.