https://neckpinch.com/authors/jingang-xiong/New arXiv papers by Jingang Xiong, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2312.15852/arxiv:2312.15852Tue, 26 Dec 2023 00:00:00 GMTJingang Xiong — We study a family of nonlinear integral flows that involve Riesz potentials on Riemannian manifolds. In the Hardy-Littlewood-Sobolev (HLS) subcritical regime, we present a precise blow-up profile exhibited by the flows. In the HLS critical regime, by introducing a dual Q curvature we demonstrate 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.Yamabe flowSingularitiesLimit spaces & RCD