https://neckpinch.com/authors/liuwei-gong/New arXiv papers by Liuwei Gong, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2602.04267/arxiv:2602.04267Wed, 04 Feb 2026 00:00:00 GMTLiuwei Gong, Sanghoon Lee, Juncheng Wei — In their seminal work, Gursky and Malchiodi introduced a non-local conformal flow in dimensions n ≥ 5 to resolve the constant Q-curvature problem. They proved sequential convergence of the flow for initial metrics with positive scalar curvature and Q-curvature, provided the energy was sufficiently small. In this paper, we prove the global convergence of the flow for arbitrary initial energy under the same positivity assumptions by establishing a non-local version of the Łojasiewicz-Simon inequality for the Paneitz-Sobolev quotient along the flow. We construct test bubbles and estimate their Paneitz-Sobolev quotients, a strategy that was carried out in the celebrated work of Brendle in the context of the Yamabe flow. We develop a more geometric and systematic proof that addresses the algebraic and computational complexity inherent in the Q-curvature and the Paneitz operator. Along the way, we derive a stability inequality for the Paneitz-Sobolev quotient using a higher-order Koiso-Bochner formula established in recent work of Bahuaud, Guenther, Isenberg, and Mazzeo.Yamabe flowOther curvature flowsScalar curvatureStability & uniqueness