Title: Blow-up Phenomenon of the prescribed Q-curvature equation on 4-manifolds in the null case

Abstract: It is widely known that if  is a closed 4-manifold with null Q-curvature and f a smooth sign-changing function with , then there exists at least one solution u to the prescribed Q-curvature equation . Here, is the positive Paneitz operator with kernel consisting of constant functions. By fixing a smooth function  satisfying  and , we then consider a family of prescribed Q-curvature equations , where  is a suitably small constant. A solution to this equation can be obtained from a minimizer  of the associated Dirichlet energy functional. We prove that the minimizer  exhibits a bubbling phenomenon in a certain limit regime as  goes to 0 and the analogy also occurs in the context of Q-curvature flows. This is a joint work with A/Prof. Ngo Quoc Anh at VNU.

Speaker: Zhang Hong, South China Normal University

Date: 14:30 2021-3-20

Wemeet ID: 567 765 321

Password: 123456

Organizer: School of Mathematical Science

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