https://neckpinch.com/authors/haoyuan-sun/New arXiv papers by Haoyuan Sun, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2605.22347/arxiv:2605.22347Thu, 21 May 2026 00:00:00 GMTHaoyuan Sun — We prove uniform diameter estimates, volume non-collapsing estimates and Gromov-Hausdorff convergence for the normalized Chern-Ricci flow on smooth complex minimal surfaces of general type, starting from an arbitrary Hermitian metric. This removes the local Kahler assumption near the null locus used in our previous work and confirms the Tosatti-Weinkove conjecture in complex dimension two. The main analytic ingredients are a surface torsion estimate, a uniform total variation bound for Delta |G|, a Green-weighted L^2 estimate for the torsion, and a linear iteration of real Poisson equations, which together give the required Green function estimates.Ricci flowGeneralized & G₂ flows(Non)collapsingKähler geometryLimit spaces & RCDMinimal & CMC surfacesAnalytic minimal model program https://neckpinch.com/papers/2604.04710/arxiv:2604.04710Mon, 06 Apr 2026 00:00:00 GMTHaoyuan Sun — We establish uniform diameter estimates and volume non-collapsing estimates for the Chern-Ricci flow on smooth Hermitian minimal models of general type, assuming the initial metric is Kähler in a neighborhood of the null locus of the canonical bundle. This yields subsequential Gromov-Hausdorff convergence, partially resolving a conjecture of Tosatti and Weinkove. When the underlying manifold is Kähler, we further prove the uniqueness of the limit space. Analytically, we overcome the difficulties posed by non-Kähler torsion in the Green's formula by exploiting our local Kähler assumption, successfully adapting recent estimates of Kähler Green's function to the Hermitian setting. To prove the uniqueness of the limit, we introduce Perelman's reduced length to the Chern-Ricci flow. By establishing a uniform Chern scalar curvature bound and an almost monotonicity formula for the reduced volume, we deduce an almost-avoidance principle for the singular set, allowing us to effectively compare the flow distance with the canonical limit distance.Ricci flowGeneralized & G₂ flowsReduced volume(Non)collapsingKähler geometryScalar curvatureLimit spaces & RCDStability & uniquenessAnalytic minimal model program