2022/09/16 by Shihang Pan, Pan, Shihang
Mathematics · #Advanced Mathematical Physics Problems #Advanced Operator Algebra Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2209.07656
openalex publication_date 2022/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we mainly study the Lieb-Thirring inequality for families of orthonormal scalar functions on the four-dimensional sphere \mathbbS4 and torus \mathbbT4 . The bounds of all the constants involved are obtained. Specifically, we prove that the costant K4(\mathbbS4) of the Lieb-Thirring inequality on the sphere \mathbbS4 satisfies 0.0844 ≤ K4(\mathbbS4)≤ 0.1728, and the constant K4(\mathbbT4) of the Lieb-Thirring inequality on the torus \mathbbT4 satisfies 0.0190 ≤ K4(\mathbbT4) ≤ 0.1222.