The Steiner Subratio in Banach Spaces

L. Burusheva

Lomonosov Moscow State University

Abstract: For every $n=2,3,\dots$, the minimum of the Steiner subratio is found for $n$-point sets in Banach spaces, and an example of a Banach space is constructed for which this minimum is attained. An example of a Banach space for which the minimum possible Steiner subratio equals $1/2$ is also constructed.

Keywords: Banach space, shortest network, minimal filling, Steiner subratio.

UDC: 517.982.256+515.124.4

Received: 02.06.2018
Revised: 15.10.2018

DOI: 10.4213/mzm12081

 English version: Mathematical Notes, 2019, 106:2, 183–190

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