Conformal metrics on 2m with constant Q-curvature and large volume
Annales de l'I.H.P. Analyse non linéaire, Volume 30 (2013) no. 6, p. 969-982

We study conformal metrics g u =e 2u |dx| 2 on 2m with constant Q-curvature Q g u (2m-1)! (notice that (2m-1)! is the Q-curvature of S 2m ) and finite volume. When m=3 we show that there exists V such that for any V[V ,) there is a conformal metric g u =e 2u |dx| 2 on 6 with Q g u 5! and vol (g u )=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(0,V m ] there is a conformal metric g u =e 2u |dx| 2 on 2m with Q g u (2m-1)!, 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.

DOI : https://doi.org/10.1016/j.anihpc.2012.12.007
Keywords: Q-curvature, Paneitz operators, GMJS operators, Conformal geometry
@article{AIHPC_2013__30_6_969_0,
     author = {Martinazzi, Luca},
     title = {Conformal metrics on $ {\mathbb{R}}^{2m}$ with constant Q-curvature and large volume},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {30},
     number = {6},
     year = {2013},
     pages = {969-982},
     doi = {10.1016/j.anihpc.2012.12.007},
     zbl = {1286.53018},
     mrnumber = {3132411},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2013__30_6_969_0}
}
Martinazzi, Luca. Conformal metrics on $ {\mathbb{R}}^{2m}$ with constant Q-curvature and large volume. Annales de l'I.H.P. Analyse non linéaire, Volume 30 (2013) no. 6, pp. 969-982. doi : 10.1016/j.anihpc.2012.12.007. http://www.numdam.org/item/AIHPC_2013__30_6_969_0/

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