In this talk, we describe some monotonicity formulas holding **along the regular level sets of suitable p?harmonic functions in asymptotically flat Riemannian 3?manifolds with a single end, with or without boundary, having nonnegative scalar curvature. Using such formulas, we obtain some geometric inequalities, including the positive mass inequality and the Riemannian Penrose inequality. The talk is based on joint works with V. Agostiniani, C. Mantegazza and L. Mazzieri.