Nihonkai Mathematical Journal

Steiner ratios for length spaces having ends

Nobuhiro Innami and Shinetsu Tamura

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Abstract

We prove that the Steiner ratios for complete locally compact length spaces having $n$ ends are less than or equal to $n/2(n-1)$. In particular, the Steiner ratio of a complete simply connected surface with a pole satisfying the Visibility axiom is $1/2$.

Article information

Source
Nihonkai Math. J., Volume 19, Number 2 (2008), 105-110.

Dates
First available in Project Euclid: 18 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.nihmj/1363634623

Mathematical Reviews number (MathSciNet)
MR2490132

Zentralblatt MATH identifier
1173.53314

Subjects
Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]
Secondary: 05C05: Trees

Keywords
Differential geometry geometry of geodesics Steiner tree Steiner ratio

Citation

Tamura, Shinetsu; Innami, Nobuhiro. Steiner ratios for length spaces having ends. Nihonkai Math. J. 19 (2008), no. 2, 105--110. https://projecteuclid.org/euclid.nihmj/1363634623


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