https://neckpinch.com/authors/huaiyu-zhang/New arXiv papers by Huaiyu Zhang, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2405.10495/arxiv:2405.10495Fri, 17 May 2024 00:00:00 GMTChang Li, Huaiyu Zhang, Xi Zhang — In this paper, we study the rigidity of eigenvalues of shring Ricci solitons. It is known that the drifted Laplacian on shrinking Ricci solitons has discrete spectrum, its eigenvalues have a lower bound and a rigidity result holds. Firstly, we show that if the n^th eigenvalue is close to this lower bound, then the n-soliton must be the trivial Gaussian soliton ℝⁿ. Secondly, we show similar results for the (n-1)^th and (n-2)^th eigenvalue under a non-collapsing condition. Lastly, we give an alomost rigidity for the k^th eigenvalue with general k. Part of our results could be viewed as an soliton (could be noncompact) analog of Theorem 1.1 (which only holds for compact manifolds) in Peterson (Invent. Math. 138 (1999): 1-21).Ricci solitons(Non)collapsingStability & uniquenessBoundaries & non-compactEigenvalues & spectrum https://neckpinch.com/papers/2110.12157/arxiv:2110.12157Sat, 23 Oct 2021 00:00:00 GMTWenshuai Jiang, Weimin Sheng, Huaiyu Zhang — In this paper, we study Ricci flow on compact manifolds with a continuous initial metric. It was known from Simon that the Ricci flow exists for a short time. We prove that the scalar curvature lower bound is preserved along the Ricci flow if the initial metric has a scalar curvature lower bound in distributional sense provided that the initial metric is W^(1,p) for some n<p≤ ∞. As an application, we use this result to study the relation between Yamabe invariant and Ricci flat metrics. We prove that if the Yamabe invariant is nonpositive and the scalar curvature is nonnegative in distributional sense, then the manifold is isometric to a Ricci flat manifold.Ricci flowRicci-flat & Calabi–YauScalar curvature