关于紧单李群上自然约化度量的最小Laplace eigenvalue
On the smallest Laplace eigenvalue for naturally reductive metrics on compact simple Lie groups
摘要：
Eldredge，Gordina和Saloff-Coste最近证明了，对于给定的紧致连通李群$G$，存在正实数$C$，使得对于$G$上的所有左不变度量$g$，$λ_1(G,g)\operatorname{diam}(G,g)^2\leq C$。本文建立了紧单李群上自然约化左不变度量的小子类的猜想。
英文摘要：
Eldredge, Gordina and Saloff-Coste recently conjectured that, for a given compact connected Lie group $G$, there is a positive real number $C$ such that $λ_1(G,g)\operatorname{diam}(G,g)^2\leq C$ for all left-invariant metrics $g$ on $G$. In this short note, we establish the conjecture for the small subclass of naturally reductive left-invariant metrics on a compact simple Lie group.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
