Calculus of Variations and Geometric Measure Theory
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M. Carioni - A. Pluda

Calibrations for minimal networks in a covering space setting

created by pluda on 05 Mar 2017
modified by carioni on 13 Apr 2019

[BibTeX]

Accepted Paper

Inserted: 5 mar 2017
Last Updated: 13 apr 2019

Journal: ESAIM Control Optim. Calc. Var.
Year: 2019

Abstract:

In this paper we define a notion of calibration for an equivalent approach to the classical Steiner problem in a covering space setting and we give some explicit examples. Moreover we introduce the notion of calibration in families: the idea is to divide the set of competitors in a suitable way, defining an appropriate (and weaker) notion of calibration. Then, calibrating the candidate minimizers in each family and comparing their perimeter, it is possible to find the minimizers of the minimization problem. Thanks to this procedure we prove the minimality of the Steiner configurations spanning the vertices of a regular hexagon and of a regular pentagon.


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