Multiplicity of singular solutions to the fractional Yamabe problem on spheres

Abstract

We prove nonuniqueness results for complete metrics with constant positive fractional curvature conformal to the round metric on $S^n\setminus S^k$, using bifurcation techniques. These are singular (positive) solutions to a non-local equation with critical non-linearity.

LaTeX2e, 18 pages, 2 figures, final (revised) version

References in corpus (1)

• Asymptotics of the Poisson kernel and Green's functions of the fractional conformal Laplacian