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We prove a sharp inequality for hypersurfaces in the ndimensional Anti-deSitter-Schwarzschild manifold for general $n \ge  3$. This inequality generalizes the classical Minkowski inequality [19] for surfaces in the three dimensional Euclidean space. The proof relies on a new monotonicity formula for inverse mean curvature flow, and uses a geometric inequality established in [4].

We study how conserved quantities such as angular momentum and center of mass evolve with respect to the retarded time at null infinity, which is described in terms of a Bondi-Sachs coordinate system. These evolution formulae complement the classical Bondi mass loss formula for gravitational radiation. They are further expressed in terms of the potentials of the shear and news tensors. The consequences that follow from these formulae are (1) Supertranslation invariance of the fluxes of the CWY conserved quantities. (2) A conservation law of angular momentum \`a la Christodoulou. (3) A duality paradigm for null infinity. In particular, the supertranslation invariance distinguishes the CWY angular momentum and center of mass from the classical definitions.

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Let $M^n$ be a complete noncompact K\"ahler manifold with nonnegative bisectional curvature and maximal volume growth, we prove that $M$ is biholomorphic to $\mathbb{C}^n$. This confirms the uniformization conjecture of Yau under the assumption $M$ has maximal volume growth.