https://neckpinch.com/authors/yuanqing-ma/New arXiv papers by Yuanqing Ma, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2606.06619/arxiv: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://neckpinch.com/papers/2109.02449/arxiv:2109.02449Mon, 06 Sep 2021 00:00:00 GMTYuanqing Ma, Bing Wang — Consider a Riemannian manifold (M^(m), g) whose volume is the same as the standard sphere (S^(m), gᵣound). If p>m/2 and ∫_M \ Rc-(m-1)g\₋^(p) dv is sufficiently small, we show that the normalized Ricci flow initiated from (M^(m), g) will exist immortally and converge to the standard sphere. The choice of p is optimal.Ricci flowLong-time existence & convergence