Title: Calibrations for minimal networks in a covering space setting,
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.