A Jang equation approach to the Penrose inequality

We introduce a generalized version of the Jang equation, designed for thegeneral case of the Penrose Inequality in the setting of an asymptotically flatspace-like hypersurface of a spacetime satisfying the dominat energy condition.The appropriate existence and regularity results are established in the specialcase of spherically symmetric Cauchy data, and are applied to give a new proofof the general Penrose Inequality for these data sets. When appropriatelycoupled with an inverse mean curvature flow, analogous existence and regularityresults for the associated system of equations in the nonspherical settingwould yield a proof of the full Penrose Conjecture. Thus it remains as animportant and challenging open problem to determine whether this system doesindeed admit the desired solutions.