The Steiner tree problem revisited through rectifiable G-currents

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.

References in corpus (1)

• Decomposition of acyclic normal currents in a metric space

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