Scalar curvature deformations with non-compact boundaries

We develop a general deformation principle for families of Riemannian metrics on smooth manifolds with possibly non-compact boundary, preserving lower scalar curvature bounds. The principle is used to strengthen boundary conditions from mean convex to totally geodesic or doubling. The deformation principle preserves other geometric properties such as completeness and a given quasi-isometry type.

As an application, we prove non-existence results for Riemannian metrics with uniformly positive scalar curvature and mean convex boundary, including some investigation of the Whitehead manifold.