Deformations of positive scalar curvature metrics

I will present three deformation results, the first of which 
is very general and goes back to Gromov, while the other two are 
specific to scalar curvature. As applications, we will discuss the 
equivalence (up to homotopy) of different boundary conditions for 
metrics of positive scalar curvature (PSC), the smoothability of 
mean-convex singularities in the space of PSC metrics, examples of 
spaces of PSC metrics with nontrivial homotopy, and the contractibility 
of certain spaces of S1-invariant PSC metrics.

This is joint work with Bernardo Hanke (Augsburg)