Abstract
We consider solutions to the equation \(\displaystyle{ (-\Delta )^{m}u = (2m - 1)!e^{2mu}\quad \text{in }\mathbb{R}^{2m}, }\) satisfying \(\displaystyle{ V:=\int _{\mathbb{R}^{2m}}e^{2mu(x)}dx <+\infty. }\) Geometrically, if u solves (1)–(2), then the conformal metric g u : = e 2u | dx | 2 has Q-curvature \(Q_{g_{u}} \equiv (2m - 1)!\) and volume V (by | dx | 2 we denote the Euclidean metric).
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The author is supported by the Swiss National Science Foundation.
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Martinazzi, L. (2015). Recent Results and Open Problems on Conformal Metrics on ℝn with Constant Q-Curvature. In: González, M., Yang, P., Gambino, N., Kock, J. (eds) Extended Abstracts Fall 2013. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-21284-5_9
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