The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

Portugaliae Mathematica

Full-Text PDF (70 KB) | Metadata | Table of Contents | PM summary
Volume 65, Issue 2, 2008, pp. 237–242
DOI: 10.4171/PM/1808

Published online: 2008-06-30

Steiner's invariants and minimal connections

Stephen Ducret[1] and Marc Troyanov[2]

(1) Ecole Polytechnique Fédérale de Lausanne, Switzerland
(2) Ecole Polytechnique Fédérale de Lausanne, Switzerland

The aim of this note is to prove that any compact metric space can be made connected at a minimal cost, where the cost is taken to be the one-dimensional Hausdorff measure.

Keywords: Metric geometry, Steiner invariant

Ducret Stephen, Troyanov Marc: Steiner's invariants and minimal connections. Port. Math. 65 (2008), 237-242. doi: 10.4171/PM/1808