Calculus of Variations and Geometric Measure Theory
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L. Martinazzi

Conformal metrics on R^{2m} with constant Q-curvature and large volume

created by martinazz on 17 Jul 2018



Inserted: 17 jul 2018
Last Updated: 17 jul 2018

Year: 2012

ArXiv: 1202.1222 PDF


We study conformal metrics on R{2m} with constant Q-curvature and finite volume. When m=3 we show that there exists V such that for any V\in V*,\infty) there is a conformal metric g on R^{6} with Q_g = Q-curvature of S^6, and vol(g)=V. This is in sharp contrast with the four-dimensional case, treated by C-S. Lin. We also prove that when $m$ is odd and greater than 1, there is a constant V_m>\vol (S^{2m}) such that for every V\in (0,V_m there is a conformal metric g on R{2m} with Qg = Q-curvature of S{2m}, vol(g)=V. This extends a result of A. Chang and W-X. Chen. When m is even we prove a similar result for conformal metrics of negative Q-curvature.

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