ETD

• analisi geometrica
• relatività generale

In this thesis 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", onecan 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 the authors proved a theoremwhich 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 in the article.