Inserted: 27 mar 2018
Last Updated: 26 oct 2020
Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
We provide monotonicity formulas for solutions to the p-Laplace equation defined in the exterior of a convex domain. A number of analytic and geometric consequences are derived, including the classical Minkowski inequality as well as new characterizations of rotationally symmetric solutions and domains. The proofs rely on the conformal splitting technique introduced by the second author in collaboration with V. Agostiniani.