2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/220646In this thesis we describe how minimal surface techniques can be used to prove the Penrose inequality in general relativity for two classes of 3-manifolds. We also describe how a new volume comparison theorem involving scalar curvature for 3-manifolds follows from these same techniques.(111 pages, 8 figures) This posting is my thesis (Stanford, 1997). I have not gotten around to publishing these results as of 2009, although I have always had the intention to do so. Since multiple papers have cited this thesis, I am posting it hereDifferential GeometryMathematical Physics53C80text