Let 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 {\protect\emph{Q}-curvature} metrics near the hyperbolic metric}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {591--614}, publisher = {Elsevier}, volume = {31}, number = {3}, year = {2014}, doi = {10.1016/j.anihpc.2013.04.008}, mrnumber = {3208456}, zbl = {1302.58012}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2013.04.008/} }
TY - JOUR AU - Li, Gang TI - Constant Q-curvature metrics near the hyperbolic metric JO - Annales de l'I.H.P. Analyse non linéaire PY - 2014 SP - 591 EP - 614 VL - 31 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2013.04.008/ DO - 10.1016/j.anihpc.2013.04.008 LA - en ID - AIHPC_2014__31_3_591_0 ER -
%0 Journal Article %A Li, Gang %T Constant Q-curvature metrics near the hyperbolic metric %J Annales de l'I.H.P. Analyse non linéaire %D 2014 %P 591-614 %V 31 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2013.04.008/ %R 10.1016/j.anihpc.2013.04.008 %G en %F 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/articles/10.1016/j.anihpc.2013.04.008/
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