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This question is related to a previous one.

Let $(M^n,g)$ be a compact Riemannian manifold with boundary. Assume it has positive scalar curvature and $\partial M$ is mean convex (positive mean curvature).

Question: Is it true that $DM$, the double of $M$, admits a metric of positive scalar curvature?

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This is true/well-known. A reference is Gromov--Lawson "Spin and scalar curvature in the presence of a fundamental group. I" (https://mathscinet.ams.org/mathscinet-getitem?mr=569070) Theorem 5.7.

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