The number of unit distances is almost linear for most norms

We prove that there exists a norm in the plane under which no n-point set determines more than O(n log n log logn) unit distances. Actually, most norms have this property, in the sense that their complement is a meager set in the metric space of all norms (with the metric given by the Hausdorff distance of the unit balls).

• Publication year

  2010

• Venue

  Unknown venue

• Publication date

  2010-07-07

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1016/j.aim.2010.09.009arXiv 1007.1095
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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