# Limits equations arising in the vacuum Einstein constraint equations using the conformal method

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Stefano GioffrÃ¨

created by pluda on 06 May 2016

11 may 2016
-- 15:30
[open in google calendar]

sala seminari, dipartimento di matematica di Pisa

**Abstract.**

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.