On the smallest Laplace eigenvalue for naturally reductive metrics on compact simple Lie groups

Lauret, Emilio

doi:10.1090/proc/14969

On the smallest Laplace eigenvalue for naturally reductive metrics on compact simple Lie groups
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by Emilio A. Lauret PDF

Proc. Amer. Math. Soc. 148 (2020), 3375-3380 Request permission

Abstract:

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 $\lambda _1(G,g)\operatorname {diam}(G,g)^2\leq C$ 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.

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