Lower bound of Schrödinger operators on Riemannian manifolds
Mael Lansade
Aix-Marseille Université, France
![Lower bound of Schrödinger operators on Riemannian manifolds cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-jst-volume-13-issue-1.png&w=3840&q=90)
Abstract
We show that a complete weighted manifold which satisfies to a relative Faber–Krahn inequality admits a trace inequality for the measure with density , with the constant depending on a Morrey norm of . From this, we obtain estimates on the lower bound of the spectrum of the Schrödinger operators with potential and positivity conditions for such operators. It also yields a Hardy inequality.
Cite this article
Mael Lansade, Lower bound of Schrödinger operators on Riemannian manifolds. J. Spectr. Theory 13 (2023), no. 1, pp. 153–199
DOI 10.4171/JST/448