Published Paper

Inserted: 6 feb 2009
Last Updated: 17 jul 2018

Journal: Math. Z.
Volume: 263
Pages: 307-329
Year: 2009

Abstract:

We classify the solutions to the equation (- \Delta)^m u=(2m-1)!e^{2mu} on R^{2m} giving rise to a metric g=e^{2u}g_{R^{2m}} with finite total $Q$-curvature in terms of analytic and geometric properties. The analytic conditions involve the growth rate of u and the asymptotic behaviour of \Delta u(x) as
x
\to \infty. As a consequence we give a geometric characterization in terms of the scalar curvature of the metric e^{2u}g_{R^{2m}} at infinity, and we observe that the pull-back of this metric to $S^{2m}$ via the stereographic projection can be extended to a smooth Riemannian metric if and only if it is round.

Keywords: Q-curvature, Paneitz operator

Download:

• classification.pdf