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 $d(o,x{)}^{-(n-2)/2}$, on complete noncompact ma…