https://neckpinch.com/authors/jie-wang/New arXiv papers by Jie Wang, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2609.18594arxiv:2609.18594Wed, 16 Sep 2026 00:00:00 GMTBing Wang, Jie Wang — As a metric measure space possessing positive Bakry-Émery curvature, a Ricci shrinker with potential function f admits a heat kernel H_f under the weighted volume measure e^(−f)dv. In this paper, we study H_f systematically and establish a series of fundamental estimates. Moreover, we clarify the equivalence between H_f and the spacetime heat kernel H(x,t;y,s) under Ricci flow induced by a Ricci shrinker. Inspired by this relation, we extend corresponding analysis tools of Ricci flows to Ricci shrinker metric measure spaces, such as Nash entropy and reduced distance. As a direct application, we prove that |∇R|=o(f^(3/2)) implies R=o(f).Ricci flowRicci solitonsPerelman entropyReduced volumeHeat kernelLimit spaces & RCD https://arxiv.org/abs/2604.02632arxiv:2604.02632Fri, 03 Apr 2026 00:00:00 GMTYi Li, Jie Wang, Pingsan Yuan, Chao Zheng — In this paper, we investigate the prescribed curvature problem associated with a special Lin-Lu-Yau curvature on finite graphs of girth at least 6. We define the corresponding Calabi flow for this curvature type, and establish an equivalent characterization of the problem, namely, the solution to the Calabi flow exists globally in time and converges if and only if there exists a weight function that realizes the prescribed curvature. In particular, for constant curvature weights, we prove that the solution to the Calabi flow exists globally in time and converges under certain topological conditions.Other curvature flowsKähler geometryKähler–Einstein & K-stabilityDiscrete & graph Ricci https://arxiv.org/abs/2308.06560arxiv:2308.06560Sat, 12 Aug 2023 00:00:00 GMTJie Wang, Youde Wang — In this paper, we study the rigidity and ε-regularity theorems of Ricci shrinkers. First we prove the rigidity of the asymptotic volume ratio and local volume around a base point of a non-compact Ricci shrinker. Next we obtain some ε-regularity theorems of local entropy and curvature, which improve the previous corresponding results essentially and use them to study the structure of Ricci shrinkers at infinity. Especially, if the curvature of a non-compact Ricci shrinker satisfies some natural integral conditions, then it is asymptotic to a cone.Ricci solitonsStability & uniquenessBoundaries & non-compact