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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
58/2013

The Steiner tree problem revisited through rectifiable G-currents

Andrea Marchese and Annalisa Massaccesi

Abstract

The Steiner tree problem seeks a connected set of minimal length containing a given set of finitely many points. We show how to formulate it as a mass-minimization problem for 1-dimensional currents with coefficients in a suitable normed group. The representation used for these currents allows to state a calibration principle for this problem. We also exhibit calibrations in some examples.

Received:
Jun 5, 2013
Published:
Jun 17, 2013
MSC Codes:
49Q15, 49Q20
Keywords:
Steiner tree problem, rectiable currents, calibrations, fkat G-chains

Related publications

inJournal
2016 Repository Open Access
Andrea Marchese and Annalisa Massaccesi

The Steiner tree problem revisited through rectifiable G-currents

In: Advances in calculus of variations, 9 (2016) 1, pp. 19-39