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