Multiplicity of singular solutions to the fractional Yamabe problem on spheres

TL;DR

This paper demonstrates the existence of multiple singular solutions to the fractional Yamabe problem on spheres, using bifurcation methods to show nonuniqueness of conformal metrics with constant positive fractional curvature.

Contribution

It introduces new nonuniqueness results for the fractional Yamabe problem on spheres with singular solutions, employing bifurcation techniques.

Findings

Nonuniqueness of solutions established

Singular solutions with constant positive fractional curvature identified

Bifurcation methods applied to non-local equations

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.