https://neckpinch.com/authors/ming-hsiao/New arXiv papers by Ming Hsiao, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2604.20224arxiv:2604.20224Wed, 22 Apr 2026 00:00:00 GMTMing Hsiao — In this paper, we establish a compactness theorem for gradient Ricci solitons with scalar curvature bounds and uniform lower bounds of harmonic coordinates. Our approach is to bootstrap regularity in harmonic coordinates by exploiting the soliton equation. As an application, we show that the regular part of any noncollapsed limit of gradient Ricci solitons with bounded Ricci curvature is smooth. Further, we show that a steady gradient Ricci soliton is asymptotically cylindrical under an 𝓛¹-decay assumption on its Ricci curvature.Ricci solitons(Non)collapsingScalar curvatureLimit spaces & RCD https://arxiv.org/abs/2512.05625arxiv:2512.05625Fri, 05 Dec 2025 00:00:00 GMTPak-Yeung Chan, Ming Hsiao — In this paper, we demonstrate certain curvature estimates on complete non-compact steady and expanding gradient Ricci solitons in higher dimensions. In the expanding case, we prove that if the Ricci curvature decays at least quadratically, then the curvature operator decays at the rate BigO(1/r²) when n=4 and BigO((log r)/r²) when n≥5. This refines the curvature bounds in a previous result by Cao-Liu-Xie, and removes the nonnegative Ricci curvature assumption in the estimates by Cao-Liu and Cao-Liu-Xie. As a geometric application, we establish the existence and uniqueness of C^(1,α) conical structure at infinity of Ricci expander with finite Ricci curvature ratio. In the steady case, using an integral estimate of the curvature, we prove that the curvature operator has at most polynomial growth when the potential function is proper and the Ricci curvature has linear decay. Moreover, we also confirm that the curvature is bounded if we further assume the Ricci curvature has super-linear decay BigO(r^(−1-ε)). As an application, we prove the existence and uniqueness of cylindrical structure at infinity of steady soliton with super-linear Ricci curvature decay and proper potential function.Ricci solitonsStability & uniquenessBoundaries & non-compact https://arxiv.org/abs/2505.23157arxiv:2505.23157Thu, 29 May 2025 00:00:00 GMTMing Hsiao — We establish a short-time existence theory for complete Ricci flows under scaling-invariant curvature bounds, starting from rotationally symmetric metrics on ℝⁿ⁺¹ that are noncollapsed at infinity, without assuming bounded curvature. As a consequence, we construct a complete Ricci flow solution coming out of a rotationally symmetric metric, which has a cone-like singularity at the origin and no minimal hypersphere centered at the origin, using an approximation method.Ricci flowSingularities(Non)collapsingWeak & singular flowsHarmonic maps & DeTurck trickRotational symmetry & warped products https://arxiv.org/abs/2504.08189arxiv:2504.08189Fri, 11 Apr 2025 00:00:00 GMTMing Hsiao, Man-Chun Lee — In this work, we study a gap phenomenon in locally conformally flat Riemannian manifolds with non-negative Ricci curvature. We construct complete solutions to the Yamabe flow that exhibit instantaneous bounded curvature as they evolve. Using this, we demonstrate that if the curvature decays quickly enough in an integral sense, then the manifold must be flat. This partially generalizes the results of Chen-Zhu and Ma.Yamabe flow