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Non-compactness of initial data sets in high dimensions.

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GTAW01 - General relativity: from geometry to amplitudes

We will discuss instability and non-compactness results for the conformal constraint equations in dimensions larger than six. These equations are obtained from the classical constraint equations of the evolution problem in General Relativity after a conformal change of variables. The system obtained in this way is a nonlinear critical system of elliptic PDEs.
We will show that in high dimensions blowing-up solutions of this system of equations naturally appear. The method is constructive, and the construction involves topological and blow-up techniques and relies on the  a priori analysis of defects of compactness for critical elliptic PDEs. A reformulation in terms of the initial-value problem will be given.

This talk is part of the Isaac Newton Institute Seminar Series series.

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