Mathematical Problems in General Relativity

Orateur: SCHOEN Richard
Localisation: Université Stanford, États-Unis
Type: Cours doctoraux
Site: Hors LAMA , IHP
Salle: Salle 005
Date de début: 05/12/2011 - 09:00
Date de fin: 05/12/2011 - 09:00

This course will introduce the Einstein equations and describe some mathematical problems which arise in their study. We will focus on areas in which recent progress has been made. Topics will include the Cauchy problem and the constraint equations. We will describe questions concerning the asymptotic behavior of solutions of the constraint equations and density theorems. These will elucidate the behavior of the energy and linear and angular momentum for asymptotically flat spacetimes. We will describe recent progress on mass/angular momentum inequalities. We will also discuss questions relating to gravitational energy and positive energy theorems as well as notions of quasilocal mass. Some of the tools here include minimal hypersurface theory, inverse mean curvature flow, and the Dirac operator.