论文标题
在四维球和圆环上的曲折不平等
Lieb-Thirring inequality on the four-dimensional sphere and torus
论文作者
论文摘要
在本文中，我们主要研究了四维球体上的正顺式标量功能$ \ mathbb {s}^{4} $和torus $ \ mathbb {t}^{4} $的lieb thirritry不平等。获得了所有相关常数的界限。具体而言，我们证明了lieb-thirring不平等的costant $ \ mathcal {k} _ {4}（\ mathbb {s}^{4}）$ \ Mathcal {k} _ {4}（\ Mathbb {s}^{4}）\ leq 0.1728，$$和常数$ \ Mathcal {k} _ {4} _ {4}（\ Mathbb {t}^{4}） \ Mathbb {t}^{4} $满足$$ 0.0190 \ leq \ mathcal {k} _ {4}（\ Mathbb {t}^{4}）\ leq 0.1222。$$
In this paper, we mainly study the Lieb-Thirring inequality for families of orthonormal scalar functions on the four-dimensional sphere $ \mathbb{S}^{4} $ and torus $ \mathbb{T}^{4} $. The bounds of all the constants involved are obtained. Specifically, we prove that the costant $ \mathcal{K}_{4}(\mathbb{S}^{4}) $ of the Lieb-Thirring inequality on the sphere $ \mathbb{S}^{4} $ satisfies $$ 0.0844 \leq \mathcal{K}_{4}(\mathbb{S}^{4})\leq 0.1728,$$ and the constant $ \mathcal{K}_{4}(\mathbb{T}^{4}) $ of the Lieb-Thirring inequality on the torus $ \mathbb{T}^{4} $ satisfies $$ 0.0190 \leq \mathcal{K}_{4}(\mathbb{T}^{4}) \leq 0.1222.$$
