Generalized S 1 Stability Theorem

We use the equivariant [Formula: see text]-bubble technique to prove that for any compact connected orientable manifold [Formula: see text] with non-empty boundary, [Formula: see text], the Yamabe invariant of [Formula: see text] is positive if and only if the Yamabe invariant of [Formula: see text] is positive. This generalizes the [Formula: see text]-stability conjecture of Rosenberg to compact manifolds with boundary.