https://neckpinch.com/authors/haozhao-li/New arXiv papers by Haozhao Li, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2610.05217arxiv:2610.05217Sun, 04 Oct 2026 00:00:00 GMTHaozhao Li, Bing Wang, Kai Zheng — We prove that the Calabi flow extends past any finite time on compact Kähler surfaces if its Sobolev constants remain uniformly bounded. Moreover, we show the long-time existence of Calabi flow in certain Kähler classes on compact Kähler surfaces when the initial Calabi energy is strictly below an explicit threshold.Other curvature flowsSingularitiesKähler geometryLong-time existence & convergenceKähler–Einstein & K-stability https://arxiv.org/abs/2606.06619arxiv:2606.06619Thu, 04 Jun 2026 00:00:00 GMTHaozhao Li, Yuanqing Ma, Kai Zheng — In this work, we establish compactness and regularity results for complete gradient Laplacian solitons of closed G₂-structures. Under a lower scalar-curvature bound and a distance-dependent bound on the gradient of the soliton potential, we prove pointed measured Gromov-Hausdorff compactness. With a uniform lower bound for the localised Perelman entropy, the Gromov-Hausdorff convergence improves to pointed C^(1,α) convergence. Our principal result shows that this C^(1,α) convergence upgrades to smooth convergence on the regular set. More precisely, after passing to a subsequence, the metrics, the defining positive 3-forms, and the soliton potentials converge smoothly on every compact subset of the regular set, and the limiting data define a gradient Laplacian soliton. The proof develops a local entropy method adapted to G₂-solitons. Since the available C^(1,α) control does not directly close an elliptic bootstrap for the G₂-soliton, and no suitable pseudolocality theorem is available in this setting, we instead use the localised Perelman's functionals. These yield an entropy ε-regularity theorem and a gap theorem for scalar-flat solitons. On the regular set, pointed C^(1,α) convergence gives an almost-Euclidean local isoperimetric inequality, which in turn verifies the required small-entropy condition automatically. The resulting curvature bounds are then combined with G₂-specific differential identities and quantitative interior estimates to control the soliton data. Finally, at the critical exponent in dimension seven, we show that a uniform weighted L^(7/2) -curvature bound then yields pointed C^∞ compactness.Generalized & G₂ flowsPerelman entropyScalar curvatureLimit spaces & RCDLong-time existence & convergenceGeometric inequalities 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/2510.14302arxiv:2510.14302Thu, 16 Oct 2025 00:00:00 GMTHaozhao Li, Linwei Zhang — In this paper, we show that on a compact Kähler manifold the Calabi flow can be extended as long as some space-time L^p integrals of the scalar curvature are bounded.Other curvature flowsKähler geometryScalar curvatureKähler–Einstein & K-stability https://arxiv.org/abs/2312.05816arxiv:2312.05816Sun, 10 Dec 2023 00:00:00 GMTHaozhao Li, Linwei Zhang, Kai Zheng — In this paper, we show that the Calabi flow can be extended as long as the L^p scalar curvature is uniformly bounded for some p>n, and on a compact extremal Kähler manifold the Calabi flow with uniformly bounded L^p(p>n) scalar curvature exists for all time and converges exponentially fast to an extremal Kähler metric.Other curvature flowsKähler geometryScalar curvatureLong-time existence & convergenceKähler–Einstein & K-stability