Cheeger deformations can be used to deform some non-negatively curved Riemannian manifolds into positively curved manifolds (e.g., sectional curvatures strictly positve), see What is a Cheeger deformation?.
I would like to ask: Is there a similar, or at least somehow comparable method of deforming a non-positively curved Riemannian manifold into a negatively curved one?
In particular, I would be very interested in such a method for compact Riemannian locally symmetric spaces of Rank $>1$, which are non-positively curved but not negatively curved.
