Minkowski-type Inequalities For Hypersurfaces In The Warped-product Manifolds

In this paper,we prove two sharp Minkowski-type inequalities for star-shaped hypersurfaces in two class of warped product manifolds,in which the Anti-de SitterSchwarzschild manifold and the Reissner-Nordstr¨om-anti-de Sitter manifold are contained.The proof mainly relies on a monotonicity formula for inverse mean curvature flow and uses a geometric inequality established by Simon Brendle in [3].This two inequalities generalizes the one for hypersurfaces in the Anti-de Sitter-Schwarzschild manifold in [4] and in the Reissner-Nordstr¨om-anti-de Sitter manifold proved in [7].