ICTP Math Associates Seminar (Zoom Meeting) - Thursday 11 February at 15:00 (Quoc Anh Ngo)

[ICTP Math Section]

ICTP Math Associates Seminar


Thursday 11 February, at 15:00, Central European Time



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Speaker: Quoc Anh Ngo (Vietnam National University)


Title: Bubbling of Q-curvature equation on 4-manifolds in the null case


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 andf ≤ 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).