This question is related to a [previous one](https://mathoverflow.net/questions/391283/positive-scalar-curvature-on-the-double-of-a-manifold).


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?
> 
> 
> 



Positive scalar curvature on the double of a manifold (assuming mean convexity of the boundary)
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.


