Teorema da massa positiva e desigualdade de Penrose para gráficos com bordo não compacto e o teorema de rigidez para hiperfícies semi-Einstein minimizantes de volume

Abstract

We'll proof the Positive Mass Theorem, non negativity and rigidity, for graphical hypersurfaces, of the Euclidean Space, with non compact boundary. Supposing spherically symmetric graphical, we'll verify that the mass will keep non negative even without assuming scalar curvature non negative, and we'll verify that the rigidity of the null mass is stable. Under additional hypothesis, we'll obtain the Penrose's Inequality for suchgraphical hypersurfaces with non compact boundary. Finally, we'll obtain a theorem of rigidity for volume-minimizing semi-Einstein hypersurfaces, wich is a generalization of the Bray-Brendle-Neves' Theorem, [8], and Barros et al., [5].