Simple counterexamples to the 3G-inequality

It is shown that the 3G-inequalityG(x,z)G(z,y)G(x,y)⩽C(|x-z|2-d+|z-y|2-d)for domains D in Rd, d⩾3, already fails to hold if D contains a spine which is defined by a function ϕ satisfying liminft↓0ϕ(t)/t=0.