“…Recently, Dai, He, Seto, Wang, and Wei (in various subsets) [4,6,9] generalized the estimate to convex domains in S n , showing that the same bound holds: λ 2 − λ 1 ≥ 3π 2 /D 2 . Very recently, the second author with coauthors [3] showed the surprising result that there is no lower bound on the fundamental gap of convex domain in the hyperbolic space with arbitrary fixed diameter. This is done by estimating the fundamental gap of some suitable convex thin strips.…”