Abstract
The author studies a family of nonlinear integral flows that involve Riesz potentials on Riemannian manifolds.In the Hardy-Littlewood-Sobolev(HLS for short)subcritical regime,he presents a precise blow-up profile exhibited by the flows.In the HLS critical regime,by introducing a dual Q curvature he demonstrates the concentration-compactness phenomenon.If,in addition,the integral kernel matches with the Green's function of a conformally invariant elliptic operator,this critical flow can be considered as a dual Yamabe flow.Convergence is then established on the unit spheres,which is also valid on certain locally conformally flat manifolds.
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