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↦λ1(G/K,g)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, SU(2), and
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.Comment: Accepted for publication in Transformation Groups. arXiv admin note:
text overlap with arXiv:2004.0035