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The Steiner tree problem revisited through rectifiable G-currents


Marchese, Andrea; Massaccesi, Annalisa (2014). The Steiner tree problem revisited through rectifiable G-currents. Advances in Calculus of Variations:19-39.

Abstract

The Steiner tree problem can be stated in terms of finding 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.

Abstract

The Steiner tree problem can be stated in terms of finding 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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:National licences > 142-005
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Analysis
Physical Sciences > Applied Mathematics
Language:English
Date:26 January 2014
Deposited On:17 Jul 2019 09:40
Last Modified:15 Apr 2021 15:07
Publisher:De Gruyter
ISSN:1864-8258
OA Status:Green
Publisher DOI:https://doi.org/10.1515/acv-2014-0022

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