Theoretical analysis demonstrates equivalent Yamabe invariant positivity in compact manifolds with boundary, indicating generalized validity for Rosenberg's stability conjecture.
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.
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Wang et al. (2026) studied this question.
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