Starts 11 Feb 2021 15:00
Ends 11 Feb 2021 16:00
Central European Time
Zoom Meeting
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Abstract: On a closed 4-manifold, given a smooth non-trivial function f, the prescribing Q-curvature equation in the null case asks to solve Pu =fe^{4u} for u,
where P is the Paneitz operator. A necessary condition for the existence of a solution to the equation is that f is sign-changing; and it is well-known that this equation always admits at least one solution if, in addition, the total integral of f is negative. As an immediate consequence, if we let f be sign-changing and
≤ ε  for sufficiently small ε, then it turns out that a solution exists.
In this talk, I will present some results on the behavior of solutions to the equation if we let ε go to zero.
This is joint work with Hong Zhang (SCNU, China).