For the SU(2) hedgehog with h=9gr/(r^3+1)^2, the reduced Faddeev-Popov operator is positive exactly for -2<g<1, with normalizable threshold zero modes at both endpoints.
Orland,Gauge-invariant coordinates on gauge-theory orbit space, Phys
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Some Remarks on the Spectral Geometry of the Gribov Horizon
For the SU(2) hedgehog with h=9gr/(r^3+1)^2, the reduced Faddeev-Popov operator is positive exactly for -2<g<1, with normalizable threshold zero modes at both endpoints.