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

LAURET, EMILIO A.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

AMER MATHEMATICAL SOC

Año: 2020 vol. 148 p. 3375 - 3380

0002-9939

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 $lambda_1(G,g)operatorname{diam}(G,g)^2leq C$ 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.