Diff. Geom, Math. Phys., PDE Seminar: Ali Hyder

  • Date: 11/14/2017
  • Time: 15:30
Ali Hyder, UBC and Univ. Basel

University of British Columbia


Conformal metrics on \mathbb{R}^n with arbitrary total Q-curvature


I will talk about the existence of solution to the Q-curvature problem



(-\Delta)^\frac n2 u=Qe^{nu}\quad\text{in }\mathbb{R}^n,\quad




where Q is a non-negative function and n>2.


Geometrically, if u is a solution to \eqref{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 \eqref{1} for every \kappa > 0.

Other Information: 

ESB 2012
Tue 14 Nov 2017, 3:30pm-4:30pm