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Advances in Calculus of Variations

Managing Editor: Duzaar, Frank / Kinnunen, Juha

Editorial Board Member: Armstrong, Scott N. / Astala, Kari / Colding, Tobias / Dacorogna, Bernard / Dal Maso, Gianni / DiBenedetto, Emmanuele / Fonseca, Irene / Finster, Felix / Gianazza, Ugo / Gursky, Matthew / Hardt, Robert / Ishii, Hitoshi / Kristensen, Jan / Manfredi, Juan / Martell, Jose Maria / McCann, Robert / Mingione, Giuseppe / Nystrom, Kaj / Pacard, Frank / Preiss, David / Riviére, Tristan / Schaetzle, Reiner / Silvestre, Luis

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IMPACT FACTOR 2016: 1.182

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1864-8266
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The Steiner tree problem revisited through rectifiable G-currents

Andrea Marchese / Annalisa Massaccesi
Published Online: 2014-07-26 | DOI: https://doi.org/10.1515/acv-2014-0022

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.

Keywords: Steiner tree problem; rectifiable currents; calibration; flat G-chains

MSC: 49Q15; 49Q20

About the article

Received: 2013-04-02

Revised: 2014-04-30

Accepted: 2014-07-09

Published Online: 2014-07-26

Published in Print: 2016-01-01


Citation Information: Advances in Calculus of Variations, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2014-0022.

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[1]
Sergio Conti, Adriana Garroni, and Annalisa Massaccesi
Calculus of Variations and Partial Differential Equations, 2015, Volume 54, Number 2, Page 1847

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