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

• Date: 11/14/2017
• Time: 15:30
Lecturer(s):
Ali Hyder, UBC and Univ. Basel
Location:

University of British Columbia

Topic:

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

Description:

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

\begin{align}\label{1}

\kappa:=\int_{\mathbb{R}^n}Qe^{nu}dx<\infty,

\end{align}

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