PDEA Seminar: The generalized Jang equation in the asymptotically anti-de Sitter setting and possible applications

Abstract: We will begin by recalling certain so called positive mass type results in the asymptotically Euclidean and asymptotically Minkowski settings and briefly discuss how the so called classical Jang equation is used in the reduction arguments used to prove them. Looking at the case of rigidity and considering the case of a so called asymptotically anti de Sitter-Schwarzschild initial data set, we motivate the analysis of the generalized Jang equation. We then discuss how one could prove a positive mass type result for asymptotically anti de Sitter-Schwarzschild initial data sets given that a coupled system of elliptic partial differential equations has a solution. Finally we look at some of the technical details involving the construction of the solution of the generalized Jang equation in this setting, such as the necessary assumptions, how the solution is constructed and its asymptotical behavior at infinity. 

Participate on site or via Zoom link, meeting ID: 67226102216

This is a seminar in the PDEs and Applications seminar series