  The recently proposed theory of "Asymptotically Free Mimetic Gravity" is
extended to the general non-homogeneous, spatially non-flat case. We present a
modified theory of gravity which is free of higher derivatives of the metric.
In this theory asymptotic freedom of gravity implies the existence of a minimal
black hole with vanishing Hawking temperature. Introducing a spatial curvature
dependent potential, we moreover obtain non-singular, bouncing modifications of
spatially non-flat Friedmann and Bianchi universes.
