Lieb-Thirring inequalities on some manifolds

TL;DR

This paper establishes improved Lieb-Thirring inequalities on specific manifolds, namely the 2D sphere and torus, and provides bounds on negative eigenvalues in the 1D periodic case.

Contribution

It introduces new Lieb-Thirring inequalities with better constants on certain manifolds and extends bounds to the 1D periodic setting.

Findings

Improved Lieb-Thirring constants on 2D sphere and torus

Bounds on negative eigenvalues in 1D periodic case

Simultaneous bound for negative trace and eigenvalues

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.