Lower bound of Schr{\"o}dinger operators on Riemannian manifolds

M Lansade

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arXiv · 2012.08841

Lower bound of Schr{\"o}dinger operators on Riemannian manifolds

M Lansade

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Abstract

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.

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M Lansade. 2020-12-16. Lower bound of Schr{\"o}dinger operators on Riemannian manifolds. https://arxiv.org/abs/2012.08841

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