The classical Minkowski inequality says the mean curvature integral of a convex surface is bounded below by the square root of its area. Using inverse mean curvature flow, Guan-Li relaxed the convexity assumption and Brendle-Hung-Wang generalized the inequality to anti-de Sitter Schwarzschild manifold. I will discuss the equality case of Minkowski inequality on static manifolds and its implication on black hole uniqueness theorem. The talk is based on joint work with Brian Harvie.