https://neckpinch.com/authors/jie-he/New arXiv papers by Jie He, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2512.04572arxiv:2512.04572Thu, 04 Dec 2025 00:00:00 GMTJie He, Haozhao Li — In this paper, we study a family of twisted Calabi flows connecting the J-flow and Calabi flow on a compact Kähler manifold with a constant scalar curvature (cscK) metric. We show that for any initial data the twisted Calabi flow near the J-flow has long time existence and converges smoothly to the cscK metric. Moreover, we show that if a twisted Calabi flow has long time existence and converges, then the nearby twisted Calabi flow with the same initial data also has long time existence and converges. These results imply the openness of the continuity method to study Chen's long time existence conjecture on (twisted) Calabi flow on cscK manifolds.Other curvature flowsKähler geometryScalar curvatureLong-time existence & convergenceKähler–Einstein & K-stability https://arxiv.org/abs/2512.02451arxiv:2512.02451Tue, 02 Dec 2025 00:00:00 GMTJie He, Haozhao Li — This paper investigates the twisted Calabi functional and the associated twisted Calabi flow on compact Kähler manifolds. Our main contributions are threefold: first, we establish the convexity of the twisted Calabi functional at its critical points; second, we prove the short-time existence of the twisted Calabi flow; and third, we demonstrate the stability of this flow in the neighborhood of twisted constant scalar curvature Kähler metrics. These results provide an analytic foundation for studying the twisted Calabi flow and resolve questions about its local behavior.Other curvature flows3-manifoldsKähler geometryScalar curvatureStability & uniquenessHarmonic maps & DeTurck trickKähler–Einstein & K-stability https://arxiv.org/abs/2303.00631arxiv:2303.00631Wed, 01 Mar 2023 00:00:00 GMTJie He, Kai Zheng — Let (M,ω) be a compact symplectic manifold. We denote by ac the space of all almost complex structure compatible with ω. ac has a natural foliation structure with the complexified orbit as leaf. We obtain an explicit formula of the Hessian of Hermitian Calabi functional at an extremal almost Kähler metric in ac. We prove that the Hessian of Hermitian Calabi functional is semi-positive definite at critical point when restricted to a complexified orbit, as corollaries we obtain some results analogy to Kähler case. We also show weak parabolicity of the Hermitian Calabi flow.Other curvature flowsKähler geometryKähler–Einstein & K-stability