Martinazzi, Luca. (2009) Classification of solutions to the higher order Liouville’s equation on {\mathbb{R}^{2m}}. Mathematische Zeitschrift, 263. pp. 307-329.
Full text not available from this repository.
Official URL: http://edoc.unibas.ch/49850/
Downloads: Statistics Overview
Abstract
We classify the solutions to the equation (−Δ) m u = (2m − 1)!e 2mu on {\mathbb{R}^{2m}} giving rise to a metric {g=e^{2u}g_{\mathbb{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 Δu at infinity. As a consequence we give a geometric characterization in terms of the scalar curvature of the metric {e^{2u}g_{\mathbb{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.
Faculties and Departments: | 05 Faculty of Science > Departement Mathematik und Informatik > Mathematik |
---|---|
UniBasel Contributors: | Martinazzi, Luca |
Item Type: | Article, refereed |
Article Subtype: | Research Article |
Publisher: | Springer |
ISSN: | 0025-5874 |
e-ISSN: | 1432-1823 |
Note: | Publication type according to Uni Basel Research Database: Journal article |
Identification Number: | |
Last Modified: | 12 Jan 2018 10:50 |
Deposited On: | 12 Jan 2018 10:50 |
Repository Staff Only: item control page