130 research outputs found
On emerging scarred surfaces for the Einstein vacuum equations
This is a follow up on our previous work in which we have presented a
modified, simpler version of the remarkable recent result of Christodoulou on
the formation of trapped surfaces. In this paper we prove two related results.
First we extend the semi-global existence result, which was at the heart of our
previous work, to an optimal range. We then use it to establish the formation
of surfaces with multiple pre-scarred angular components
Stable blow up dynamics for the critical co-rotational Wave Maps and equivariant Yang-Mills problems
We exhibit stable finite time blow up regimes for the energy critical
co-rotational Wave Map with the S^2 target in all homotopy classes and for the
critical equivariant SO(4) Yang-Mills problem. We derive sharp asymptotics on
the dynamics at the blow up time and prove quantization of the energy focused
at the singularity
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