• currents
• Lipschitz functions
• Steiner problem

In the first part of the thesis we find an adapted version of the Rademacher theorem of differentiability of Lipschitz functions, when the Lebesgue measure on the euclidean space is replaced by a generical Radon measure.

In the second part of the thesis we explain how to understand the Steiner tree problem as a mass minimization problem in a family of rectifiable currents with coefficients in a normed group and we exhibit some calibrations in order to prove the absolute minimaity of some concrete configurations.

The common point of this problems is a substantial use of the Theory of Currents as a tool for proofs