  We consider the adiabatic evolution of glassy states under external
perturbations. Although the formalism we use is very general, we focus here on
infinite-dimensional hard spheres where an exact analysis is possible. We
consider perturbations of the boundary, i.e. compression or (volume preserving)
shear-strain, and we compute the response of glassy states to such
perturbations: pressure and shear-stress. We find that both quantities
overshoot before the glass state becomes unstable at a spinodal point where it
melts into a liquid (or yields). We also estimate the yield stress of the
glass. Finally, we study the stability of the glass basins towards breaking
into sub-basins, corresponding to a Gardner transition. We find that close to
the dynamical transition, glasses undergo a Gardner transition after an
infinitesimal perturbation.
