Constant Q-curvature metrics near the hyperbolic metric
Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 3, p. 591-614
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Let (M,g) be a Poincaré–Einstein manifold with a smooth defining function. In this note, we prove that there are infinitely many asymptotically hyperbolic metrics with constant Q-curvature in the conformal class of an asymptotically hyperbolic metric close enough to g. These metrics are parametrized by the elements in the kernel of the linearized operator of the prescribed constant Q-curvature equation. A similar analysis is applied to a class of fourth order equations arising in spectral theory.

@article{AIHPC_2014__31_3_591_0,
     author = {Li, Gang},
     title = {Constant Q-curvature metrics near the hyperbolic metric},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {31},
     number = {3},
     year = {2014},
     pages = {591-614},
     doi = {10.1016/j.anihpc.2013.04.008},
     zbl = {1302.58012},
     mrnumber = {3208456},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2014__31_3_591_0}
}
Li, Gang. Constant Q-curvature metrics near the hyperbolic metric. Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 3, pp. 591-614. doi : 10.1016/j.anihpc.2013.04.008. http://www.numdam.org/item/AIHPC_2014__31_3_591_0/

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