论文标题
紧凑型riemannian歧管的直径和拉普拉斯特征值估计值
Diameter and Laplace eigenvalue estimates for compact homogeneous Riemannian manifolds
论文作者
论文摘要
让$ g $是一个紧凑的连接谎言组，让$ k $为$ g $的封闭子组。在本文中，我们研究功能性$ g \mapstoλ_1（g/k，g）\ permatatorName {diam}（diam}（g/k，g）^2 $在$ g $ -invariant $ g $ on $ g/k $的$ g $ -invariant $ g $之间。 Eldredge，Gordina和Saloff-Coste在2018年提出了这一主张时，当$ K $微不足道时。到目前为止，唯一已知的案例是$ g $是Abelian，$ \ operatotorname {su}（2）$和$ \ operatatorName {so}（3）$。在本文中，我们证明了每个紧凑型均质空间$ g/k $具有无数性各向同性表示的存在。
Let $G$ be a compact connected Lie group and let $K$ be a closed subgroup of $G$. In this paper we study whether the functional $g\mapsto λ_1(G/K,g)\operatorname{diam}(G/K,g)^2$ is bounded among $G$-invariant metrics $g$ on $G/K$. Eldredge, Gordina, and Saloff-Coste conjectured in 2018 that this assertion holds when $K$ is trivial; the only particular cases known so far are when $G$ is abelian, $\operatorname{SU}(2)$, and $\operatorname{SO}(3)$. In this article we prove the existence of the mentioned upper bound for every compact homogeneous space $G/K$ having multiplicity-free isotropy representation.
