https://neckpinch.com/authors/yuchen-bi/New arXiv papers by Yuchen Bi, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2106.03137/arxiv:2106.03137Sun, 06 Jun 2021 00:00:00 GMTYuchen Bi, Jiayu Li — In this paper, we study the prescribed Q-curvature flow equation on a arbitrary even dimensional closed Riemannian manifold (M,g), which was introduced by S. Brendle in, where he proved the flow exists for long time and converges at infinity if the GJMS operator is weakly positive with trivial kernel and ∫_M Qdμ< (n-1)!Vol( Sⁿ ). In this paper we study the critical case that ∫_M Qdμ= (n-1)!Vol( Sⁿ ), we will prove the convergence of the flow under some geometric hypothesis. In particular, this gives a new proof of Li-Li-Liu's existence result in in dimensiona 4 and extend the work of Li-Zhu in dimension 2 to general even dimensions. In the proof, we give a explicit expression of the limit of the corresponding energy functional when the blow up occurs.Other curvature flowsSingularities