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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. The recently proposed theory of "Asymptotically Free Mimetic Gravity" is extended to the general non‐homogeneous, spatially non‐at case. The authors 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, non‐singular, bouncing modifications of spatially non‐at Friedmann and Bianchi universes are obtained. [ABSTRACT FROM AUTHOR]