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

Martinazzi, Luca. (2009) Classification of solutions to the higher order Liouville’s equation on {\mathbb{R}^{2m}}. Mathematische Zeitschrift, 263. pp. 307-329.

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Official URL: http://edoc.unibas.ch/49850/

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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

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