Abstract
We describe some recently discovered monotonicity formulas holding along the level set flow of harmonic and p-harmonic functions. The main geometric implications will then be discussed, including Willmore-type inequalities, Minkowski inequalities and, time permitting, an optimal version of Huisken’s isoperimetric inequality for three-manifolds with nonnegative Ricci curvature. The results are obtained in collaboration with V. Agostiniani, M. Fogagnolo and A. Pinamonti.
