Detecting the completeness of a Finsler manifold via potential theory for its infinity Laplacian
Channel: ICTP Mathematics
Date: 2021-03-10

Speaker: Quoc Anh Ngo (Vietnam National University)


Math Seminar


 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
f ≤ 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).