Calculus of Variations and Geometric Measure Theory

A. Marchese - A. Massaccesi

The Steiner tree problem revisited through rectifiable $G$-currents

created by marchese on 24 Sep 2012
modified by massaccesi on 12 Jan 2016


Published Paper

Inserted: 24 sep 2012
Last Updated: 12 jan 2016

Journal: Advances in Calculus of Variations
Volume: 9
Number: 1
Pages: 19-39
Year: 2016
Doi: 10.1515/acv-2014-0022


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.