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Abstract: Let (M,g) be a compact Riemannian manifold of dimension $n\geq 3$. The $\sigma_k$-Yamabe problem is concerned with finding metric of constant $\sigma_k$-curvature in the conformal class of g. The compactness of the $\sigma_k$-Yamabe problem is still widely open when $n/2> k\geq 2$. We will present a non-compactness result for the $\sigma_2$-Yamabe problem when n is large. This is a joint work with Bin Deng and Juncheng Wei.

Seminar website:  Nonlinear Analysis Seminar (https://sites.math.rutgers.edu/~yyli/NonlinearAnalysisSeminar.html)