Reports de recercahttp://hdl.handle.net/2117/797942024-04-22T15:23:19Z2024-04-22T15:23:19ZFurther results on the fractional Yamabe problem: the umbilic caseGonzález Nogueras, María del Marhttp://hdl.handle.net/2117/277102020-07-23T21:20:14Z2015-05-04T10:37:24ZFurther results on the fractional Yamabe problem: the umbilic case
González Nogueras, María del Mar
We prove some existence results for the fractional Yamabe problem in the case that the boundary manifold is umbilic, thus covering some of the cases not considered by Gonz alez and Qing. These are inspired by the work of Coda-Marques on the boundary Yamabe problem but, in addition, a careful understanding of the behavior at in nity for asymptotically hyperbolic metrics is required
preprint
2015-05-04T10:37:24ZGonzález Nogueras, María del MarWe prove some existence results for the fractional Yamabe problem in the case that the boundary manifold is umbilic, thus covering some of the cases not considered by Gonz alez and Qing. These are inspired by the work of Coda-Marques on the boundary Yamabe problem but, in addition, a careful understanding of the behavior at in nity for asymptotically hyperbolic metrics is requiredAsymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equationsGonzález Nogueras, María del MarFang, Yihttp://hdl.handle.net/2117/275632020-07-23T21:08:39Z2015-04-24T09:05:51ZAsymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equations
González Nogueras, María del Mar; Fang, Yi
In this paper, we analyze the asymptotic behavior of Palais-Smale sequences associated to fractional Yamabe type equations on an asymptotically hyperbolic Riemannian manifold. We prove that Palais-Smale sequences can be decomposed into the solution of the limit equation plus a finite number of bubbles, which are the rescaling of the fundamental solution for the fractional Yamabe equation on Euclidean space. We also verify the non-interfering fact for multi-bubbles.
preprint
2015-04-24T09:05:51ZGonzález Nogueras, María del MarFang, YiIn this paper, we analyze the asymptotic behavior of Palais-Smale sequences associated to fractional Yamabe type equations on an asymptotically hyperbolic Riemannian manifold. We prove that Palais-Smale sequences can be decomposed into the solution of the limit equation plus a finite number of bubbles, which are the rescaling of the fundamental solution for the fractional Yamabe equation on Euclidean space. We also verify the non-interfering fact for multi-bubbles.