Proposition 3 is open in the C2 × C1-topology on initial data and
is open in the
C2 × C1-topology on the subset of initial data satisfying Equation (49
).
It is of interest to note that the topology can be weakened somewhat if the only information of interest concerning the asymptotics is that the asymptotic velocity is different from 1. In fact, [79, Proposition 1.16, p. 988] states:
Proposition 4 Given , there is an open neighborhood of the initial data for
in the
C1 × C0 topology such that for each corresponding solution
,
for all
.
Recall that an asymptotic velocity different from 1 implies curvature blow up.
http://www.livingreviews.org/lrr-2010-2 |
Living Rev. Relativity 13, (2010), 2
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