30 citations · 47 across the 18 of their papers we have counts for
4 papers · 1 filter
A note on the critical Laplace Equation and Ricci curvature
Mattia Fogagnolo, Andrea Malchiodi, Lorenzo Mazzieri
We study strictly positive solutions to the critical Laplace equation \[ - Δu = n(n-2) u^{\frac{n+2}{n-2}}, \] decaying at most like , on complete noncompact ma…
Strict starshapedness of solutions to the horizontal p-laplacian in the Heisenberg group
Mattia Fogagnolo, Andrea Pinamonti
We examine the geometry of the level sets of particular horizontally -harmonic functions in the Heisenberg group. We find sharp, natural geometric conditions ensuring that the l…
Minkowski Inequalities via Nonlinear Potential Theory
Virginia Agostiniani, Mattia Fogagnolo, Lorenzo Mazzieri
In this paper, we prove an extended version of the Minkowski Inequality, holding for any smooth bounded set , . Our proof relies on the discovery of…
Geometric aspects of p-capacitary potentials
Mattia Fogagnolo, Lorenzo Mazzieri, Andrea Pinamonti
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, in…