%0 Journal Article
%T The Graphs Cases of the Riemannian Positive Mass and Penrose Inequalities in All Dimensions
%A Mau-Kwong George Lam
%J Mathematics
%D 2010
%I arXiv
%X We consider complete asymptotically flat Riemannian manifolds that are the graphs of smooth functions over $\mathbb R^n$. By recognizing the scalar curvature of such manifolds as a divergence, we express the ADM mass as an integral of the product of the scalar curvature and a nonnegative potential function, thus proving the Riemannian positive mass theorem in this case. If the graph has convex horizons, we also prove the Riemannian Penrose inequality by giving a lower bound to the boundary integrals using the Aleksandrov-Fenchel inequality.
%U http://arxiv.org/abs/1010.4256v1