Classification of solutions to the higher order Liouville's equation on R^{2m}

Details Classification of solutions to the higher order Liouville's equation on R^{2m} Classification of solutions to the higher order Liouville's equation on R^{2m}

2008-01-17

arxiv.org/abs/0801.2729v1

Math. Z. (2009)

Mathematics

Analysis of PDEs

Scientific paper

10.1007/s00209-008-0419-1

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.

Affiliated with

Also associated with

No associations

Rating

Classification of solutions to the higher order Liouville's equation on R^{2m} does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Classification of solutions to the higher order Liouville's equation on R^{2m}, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Classification of solutions to the higher order Liouville's equation on R^{2m} will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-393568