In 2006, Krieger, Schlag and Tataru (KST) constructed a family of type II blow up solutions to the 2+1 dimensional wave map equation with unit sphere as its target. This construction provides the first example of blow up solutions to the energy-critical Wave Maps. A key feature of this family is that it exhibits a continuum of blow up rates. However, from the way it was constructed, the stability of this family was not clear and it was believed to be non-generic. In this talk I will present our recent work on proving the stability and rigidity of the KST family, beyond the equivariant setting. This is based on joint works with Joachim Krieger and Wilhelm Schlag.

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