Nonstandard $n$distances based on certain geometric constructions
Abstract
The concept of $n$distance was recently introduced to generalize the classical definition of distance to functions of $n$ arguments. In this paper we investigate this concept through a number of examples based on certain geometrical constructions. In particular, our study shows to which extent the computation of the best constant associated with an $n$distance may sometimes be difficult and tricky. It also reveals that two important graph theoretical concepts, namely the total length of the Euclidean Steiner tree and the total length of the minimal spanning tree constructed on $n$ points, are instances of $n$distances.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.06807
 Bibcode:
 2021arXiv211006807K
 Keywords:

 Mathematics  Metric Geometry;
 Primary 39B72;
 Secondary 26D99