We prove Lieb–Thirring inequalities with improved constants on the two-dimensional sphere and the two-dimensional torus . In the one-dimensional periodic case we obtain a simultaneous bound for the negative trace and the number of negative eigenvalues.
Cite this article
Alexei A. Ilyin, Lieb–Thirring inequalities on some manifolds. J. Spectr. Theory 2 (2012), no. 1, pp. 57–78DOI 10.4171/JST/21