Lieb-Thirring constant on the sphere and on the torus
Alexei Ilyin, Ari Laptev, and Sergey Zelik
TL;DR
This paper establishes improved Lieb-Thirring inequalities for orthonormal functions on the 2D sphere and torus, enhancing previous bounds with new constants.
Contribution
It provides the first proof of Lieb-Thirring inequalities with improved constants specifically for the 2D sphere and torus.
Findings
Improved Lieb-Thirring constants on the 2D sphere.
Enhanced bounds for orthonormal families on the torus.
New techniques for scalar and vector functions.
Abstract
We prove on the 2D sphere and on the 2D torus the Lieb-Thirring inequalities with improved constants for orthonormal families of scalar and vector functions.
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