References for minimizers of energy in metric spaces

Question

As the title suggests, do you know some literature, books, articles or notes, that treats the connection between geodesic in a metric space and the energy associated to the curves? In particular, I am interested in some sort of $p$-energy, like the integral of the $p$-th power of the metric derivative of a curve, or something like that, and also to the relation to the ones that minimize the legth. Is there any source that treats this particular case, if they exist?