https://neckpinch.com/authors/chang-li/New arXiv papers by Chang Li, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2602.19748arxiv:2602.19748Mon, 23 Feb 2026 00:00:00 GMTChang Li, Aijin Lin, Liangming Shen — Let S be an oriented closed surface with a cellular decomposition 𝓓 and a weight Φ∈(0, π). It is crucial to determine when S supports an ideal 𝓓-type circle pattern 𝓟 with the exterior intersection angles given by Φ. Rivin, Bobenko-Springborn and Ge-Hua-Zhou provided perfect solutions and gave wonderful criteria for the existence and uniqueness of ideal circle patterns. However, all criteria established by Rivin, Bobenko-Springborn and Ge-Hua-Zhou are extremely difficult to verify for the given cellular decomposition 𝓓 and the weight Φ. In this paper, we introduce the character 𝓛(𝓓,Φ) depends only on the data of the weighted cellular decomposition (𝓓, Φ) on S, and give some quite simple criteria for the existence of ideal circle patterns realizing (𝓓,Φ). It seems that our character-type criteria are the first conditions totally different from criteria of Rivin, Bobenko-Springborn and Ge-Hua-Zhou, and provide more easily verifiable criteria. Our new character-type theorems may be of some independent interest. As an application, we give a new descriptions of the curvature image set K(ℝ^N_(>0)). To approach our results, we shall use the combinatorial Ricci flows with ideal circle patterns introduced by Ge-Hua-Zhou as a fundamental tool. The main difficulty in the proof of our results is to establish the compactness of the solution to the flows. To circumvent the difficulty, we borrow the techniques developed by Ge and his collaborators.Ricci flowLimit spaces & RCDStability & uniquenessDiscrete & graph Ricci https://arxiv.org/abs/2505.05925arxiv:2505.05925Fri, 09 May 2025 00:00:00 GMTChang Li, Yangxiang Lu, Hao Yu — Since the fundamental work of Chow-Luo, Ge et al., the combinatorial curvature flow methods became a basic technique in the study of circle pattern theory. In this paper, we investigate the combinatorial Ricci flow with prescribed total geodesic curvatures in spherical background geometry. For infinite cellular decompositions, we establish the existence of a solution to the flow equation for all time. Furthermore, under an additional condition, we prove that the solution converges as time tends to infinity. To the best of our knowledge, this is the first study of an infinite combinatorial curvature flow in spherical background geometry.Ricci flowOther curvature flowsDiscrete & graph Ricci https://arxiv.org/abs/2405.10495arxiv: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