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 |
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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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