A fractional conformal curvature flow on the unit sphere

Abstract

We study a fractional conformal curvature flow on the standard unit sphere and prove a perturbation result of the fractional Nirenberg problem with fractional exponent $\sigma \in (1/2,1)$. This extends the result of Chen-Xu (Invent. Math. 187, no. 2, 395-506, 2012) for the scalar curvature flow on the standard unit sphere.

An intermediate version, still needs to be updated

References in corpus (5)

• A Quartic Conformally Covariant Differential Operator for Arbitrary Pseudo-Riemannian Manifolds (Summary)
• Asymptotic behavior of Palais-Smale sequences associated with fractional Yamabe type equations
• Sharp constants in weighted trace inequalities on Riemannian manifolds
• Convergence of the fractional Yamabe flow for a class of initial data
• Weak and smooth solutions for a fractional Yamabe flow: the case of general compact and locally conformally flat manifolds