Lieb–Thirring inequalities on some manifolds
Alexei A. Ilyin
Keldysh Institute of Applied Mathematics, Moscow, Russian Federation
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Abstract
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. 57–78
DOI 10.4171/JST/21