A gluing approach for the fractional Yamabe problem with isolated singularities

Abstract

We construct solutions for the fractional Yamabe problem that are singular at a prescribed number of isolated points. This seems to be the first time that a gluing method is successfully applied to a non-local problem. The main step is an infinite-dimensional Lyapunov-Schmidt reduction method, that reduces the problem to an (infinite dimensional) Toda type system.

References in corpus (2)

• Asymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equations
• Non-local Curvature and Topology of Locally Conformally Flat Manifolds