Master Degree Project Presentation: Solutions Of 2D Jang Equation In The Rotationally Symmetric Asymptotically Hyperbolic Setting

Abstract: We study 2-dimensional asymptotically hyperbolic rotationally symmetric initial data sets for Einstein equations of General Relativity. For this initial data, we construct a blow-up solution to the Jang equation which is a prescribed mean curvature equation relevant in the context of positive mass theorems. We then proceed to a detailed analysis of the asymptotic behavior of the solutions near infinity using suitable sub- and supersolutions. Based on our results, we argue that the Jang equation reduction method cannot be applied to prove the positivity of mass for 2-dimensional asymptotically hyperbolic initial data sets, unless substantially modified.