The Steiner tree problem revisited through rectifiable G-currents

Andrea Marchese and Annalisa Massaccesi

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Submission date: 05. Jun. 2013
Pages: 31
published in: Advances in calculus of variations, 9 (2016) 1, p. 19-39 
DOI number (of the published article): 10.1515/acv-2014-0022
Bibtex
MSC-Numbers: 49Q15, 49Q20
Keywords and phrases: Steiner tree problem, rectiable currents, calibrations, fkat G-chains
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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.