On perturbations of the fractional Yamabe problem

Abstract

The fractional Yamabe problem, proposed by Gonzalez and Qing (Analysis PDE 6:1535–1576, 2013), is a geometric question which concerns the existence of metrics with constant fractional scalar curvature. It extends the phenomena which were discovered in the classical Yamabe problem and the boundary Yamabe problem to the realm of nonlocal conformally invariant operators. We investigate a non-compactness property of the fractional Yamabe problem by constructing bubbling solutions to its small perturbations.