The Graph Cases of the Riemannian Positive Mass and Penrose Inequalities in All Dimensions
Repository Usage Stats
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. We also prove the ZAS inequality for graphs in Minkowski space. Furthermore, we define a new quasi-local mass functional and show that it satisfies certain desirable properties.
Positive mass theorem
More InfoShow full item record
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 United States License.
Rights for Collection: Duke Dissertations