Conformal metrics on \({R}^n\) with arbitrary total \(Q\)curvature
Speaker 
Dr. Ali Hyder,Department of Mathematics and Informatics
University of Basel, Switzerland


When 
Jul 13, 2017
from 04:00 PM to 05:00 PM 
Where  LH 006 
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Abstract: I will talk about the existence of solution to the \(Q\)curvature problem
\((1)\)
\((\Delta)\)\(^\frac n2\) u=\(Qe\)\(^{nu}\)\(\quad\text{in }\)\(\mathbb{R}^n,\)\(\quad \kappa:\)=\(\int_{\mathbb{R}^n}\)\(Qe^{nu}dx\)\(<\infty,\)
where \(Q\) is a nonnegative function and \(n>2\). Geometrically, if \(u\) is a solution to \((1)\) then \(Q\) is the \(Q\)curvature of the conformal metric \(g_u\) = \(e^{2u}\)\(dx^2\) \((dx^2\) is the Euclidean metric on \(\mathbb{R}^n)\), and \(\kappa\) is the total \(Q\)curvature of \(g_u\).
Under certain assumptions on \(Q\) around origin and at infinity, we prove the existence of solution to \((1) \)for every \(\kappa\) > \(0\).