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SUMMARY:Mapping Solutions to the Constraint Equations
DTSTART;VALUE=DATE-TIME:20200117T130000Z
DTEND;VALUE=DATE-TIME:20200117T140000Z
DTSTAMP;VALUE=DATE-TIME:20220819T145452Z
UID:indico-event-5435@indico.math.cnrs.fr
DESCRIPTION:We study initial data in General Relativity\, which are define
d as solutions to the constraint equations. The focus in this talk is a mo
dified version of the conformal method proposed by David Maxwell. While th
e model seems more strongly justified from a geometrical standpoint\, the
resulting system becomes significantly more difficult to solve\; it presen
ts critical nonlinear terms\, including gradient terms. We describe existe
nce and stability while working in dimensions 3\,4 and 5\, under smallness
assumptions and in the presence of a scalar field with positive potential
. The tools we use are related to obtaining a priori estimates (compactnes
s results) and a fixed-point theorem.\n\nhttps://indico.math.cnrs.fr/event
/5435/
LOCATION:Bât E2 1180
URL:https://indico.math.cnrs.fr/event/5435/
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