  We derive local and global monotonic quantities associated to $p$-harmonic
functions on manifolds with nonnegative scalar curvature. As applications, we
obtain inequalities relating the mass of asymptotically flat $3$-manifolds, the
$p$-capacity and the Willmore functional of the boundary. As $ p \to 1$, one of
the results retrieves a classic relation that the ADM mass dominates the
Hawking mass if the surface is area outer-minimizing.

Differential Geometry;General Relativity and Quantum Cosmology;Analysis of PDEs