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Abstract: Consider the compact Riemannian manifold \((M,g)\) of dimension \(n\geq 5\). The \(\sigma_2\) Yamabe problem seeks to find a conformal metric to \(g\) that has a constant \(\sigma_2\) curvature. Sheng-Trudinger-Wang have previously proved the existence of such a metric when \(n\geq 5\), while Ge-Wang have provided a constructive proof for \(n\geq 9\). In this talk, we will present a constructive proof for the case \(n=8\) and discuss the obstruction for such construction when \(5\l eq n\leq 7\). The proof is a joint work with Bin Deng and Juncheng Wei.

Seminar website:  Learning Seminar on PDE and Applications     (https://sites.math.rutgers.edu/~yyli/Learningseminar.html)