The Riemannian Penrose Inequality

In this thesis, we aim to prove the Riemannian Penrose Inequality for asymptotically flat Riemannian manifolds with connected outermost minimal surface. To do so, we consider the geometric flow given by the level sets of a solution to a variant of the p-laplacian equation, then establish the monotonicity of a quasi-local mass function along the flow and use it to obtain the inequality. A similar strategy was first used in the article of Agostiniani, Mantegazza, Mazzieri, Oronzio on the RPI, which we aim to simplify through a more intuitive monotonicity formula.