Positive scalar curvature on manifolds with boundary and their doubles

This paper is about positive scalar curvature on a compact manifold X with non-empty boundary partial derivative X. In some cases, we completely answer the question of when X has a positive scalar curvature metric which is a product metric near. partial derivative X, or when X has a positive scalar curvature metric with positive mean curvature on the boundary, and more generally, we study the relationship between boundary conditions on partial derivative X for positive scalar curvature metrics on X and the positive scalar curvature problem for the double M = Dbl( X,partial derivative X).