11 may 2016 -- 15:30 [open in google calendar]
sala seminari, dipartimento di matematica di Pisa
In this seminar, we deal with the Einstein problem in general relativity, treating in particular the vacuum case. Using a trick developed by Choquet-Bruhat and Lichnerowicz - the well known "conformal method" - one can write the vacuum Einstein equations as a couple of differential equations, called constraint equations: a Yamabe-like scalar equation with a nonlinearity term, and a vector equation coupled to the first. In an article written in 2011 by Gicquaud, Humbert, Dahl it is proven a theorem which states that either the constraint equations admit solutions or another differential equation, a limit one admits a non-trivial solution. Our aim is to present this problem, explain the main ideas and present an attempt to prove non-existence theorems for the limit equations based on a fine analysis of the proof made article.