MiS Preprint Repository

The Penrose conjecture of general relativity, in its purely Riemannian case, states the following: in an asymptotically flat 3-manifold of nonnegative scalar curvature, the area of each outermost minimal surface is bounded by $16\pi m^2$, where $m$ is the ADM mass associated to the infinite region. We develop a weak existence and uniqueness theory of the inverse mean curvature flow put forward by Geroch and Jang-Wald, and use it to prove this inequality, although the evolving surfaces jump around in the manifold. A corollary is the positive mass theorem of Schoen and Yau.