  We show that a weighted manifold which admits a relative Faber Krahn
inequality admits the Fefferman Phong inequality V $\psi$, $\psi$ $\le$ CV
$\psi$ 2 , with the constant depending on a Morrey norm of V , and we deduce
from it a condition for a L 2 Hardy inequality to holds, as well as conditions
for Schr{\"o}dinger operators to be positive. We also obtain an estimate on the
bottom of the spectrum for Schr{\"o}dinger operators.
