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In this paper, we use the inverse mean curvature flow to establish an optimal Minkowski type inquality, weighted Alexandrov-Fenchel inequality for the mean convex star shaped hypersurfaces in Reissner-Nordström-anti-deSitter manifold and Penrose type inequality for asymptotically locally hyperbolic manifolds in which can be realized as graphs over Reissner-Nordström-anti-deSitter manifold.2010 Mathematics Subject Classification. 53C44, 53C42.

In this paper, we consider nonhomogeneous inverse Gauss curvature flows in hyperbolic space H 3 \mathbb {H}^{3} . We prove that if the initial hypersurface Σ 0 \Sigma _0 has nonnegative scalar curvature, then the evolving surface Σ t \Sigma _{t} has nonnegative scalar curvature along the flow for t > 0 t>0 . The solution of the flow exists for all time and becomes more and more umbilic as t → ∞ t\rightarrow \infty .

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