Calculus of Variations and Geometric Measure Theory
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Conformal metrics on $\mathbb{R}^n$ with arbitrary total $Q$-curvature

Ali Hyder

created by malchiodi on 01 Dec 2016
modified on 05 Dec 2016

6 dec 2016 -- 11:30   [open in google calendar]

Scuola Normale Superiore, Aula Tonelli



I will talk about the existence of solutions to the problem $(-\Delta)^{n/2} u = Q e^{n u}$ in $\mathbb{R}^n$, and such that $\kappa := \int_{\mathbb{R}^n} Q e^{n u} dx < \infty$, where $Q$ is a non-negative function and $n > 2$. Geometrically, if $u$ is a solution to the above equation then $Q$ is the Q-curvature of the conformal metric $g_u = e^{2 u} \mid \! \! d x \mid^2$. Under certain assumptions on $Q$ around origin and at infinity, we prove the existence of solution to the above equation for every $\kappa > 0$.

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