Concentration phenomena for prescribed Q-curvature problems

Ali Hyder, Johns Hopkins University

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Prescribed Q-curvature problems are higher order analog of the Gaussian curvature equation. It was shown by Adimurthi, Robert and Struwe that in the fourth order case, blow-up can occur on a three dimensional manifold, which is a zero set of a non-positive biharmonic function. I will talk about quantization of the total Q-curvature and characterization of the blow-up set.