Lower bound of Schr{ö}dinger operators on Riemannian manifolds

英文摘要：

We show that a weighted manifold which admits a relative Faber Krahn inequality admits the Fefferman Phong inequality V $ψ$, $ψ$ $\le$ CV $ψ$ 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{ö}dinger operators to be positive. We also obtain an estimate on the bottom of the spectrum for Schr{ö}dinger operators.