https://neckpinch.com/authors/yingbo-han/New arXiv papers by Yingbo Han, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2605.20852arxiv:2605.20852Wed, 20 May 2026 00:00:00 GMTShu-Cheng Chang, Yingbo Han, Chien Lin, Chin-Tung Wu — In this paper, we first confirm the Hamilton-Tian conjecture for the Sasaki-Ricci flow in a compact transverse Fano quasi-regular Sasakian 5-manifold with klt foliation singularities. Secondly, we derive the compactness theorem of Sasaki-Ricci solitons on transverse Fano quasi-regular Sasakian 5-manifolds. Then,by the second Sasakian structure theorem, we confirm the Hamilton-Tian conjecture for a compact transverse Fano Sasakian 5-manifold. With its applications, we show that the gradient Sasaki-Ricci soliton orbifold metric on a compact Sasakian 5-manifold is Sasaki-Einstein if M is transverse K-stable.Ricci flowRicci solitonsSingularitiesKähler geometryLimit spaces & RCDAnalytic minimal model programSasakian & contact geometry https://arxiv.org/abs/2508.13495arxiv:2508.13495Tue, 19 Aug 2025 00:00:00 GMTShu-Cheng Chang, Yingbo Han, Chin-Tung Wu — In this paper, we study the geometry and topology of complete gradient shrinking Sasaki-Ricci solitons. We first prove that they must be connected at infinity. This is a Sasaki analogue of gradient shrinking Kähler-Ricci solitons. Secondly, with the positive sectional curvature or positive transverse holomorphic bisectional curvature, we show that they must be compact. All results are served as a generalization of Perelman in dimension three, of Naber in dimension four, and of Munteanu-Wang in all dimensions, respectively.Ricci solitonsKähler–Ricci solitons3-manifolds4-manifoldsSphere theoremsKähler geometrySasakian & contact geometry https://arxiv.org/abs/2306.03683arxiv:2306.03683Wed, 19 Apr 2023 00:00:00 GMTShu-Cheng Chang, Yingbo Han, Chin-Tung Wu — Recently, there are a great deal of work done which connects the Legendrian isotopic problem with contact invariants. The isotopic problem of Legendre curve in a contact 3-manifold was studies via the Legendrian curve shortening flow which was introduced and studied by K. Smoczyk. On the other hand, in the SYZ Conjecture, one can model a special Lagrangian singularity locally as the special Lagrangian cones in C^3. This can be characterized by its link which is a minimal Legendrian surface in the 5-sphere. Then in these points of view, in this paper we will focus on the existence of the long-time solution and asymptotic convergence along the Legendrian mean curvature flow in higher dimensional η-Einstein Sasakian (2n+1)-manifolds under the suitable stability condition due to the Thomas-Yau conjecture.Mean curvature flowCurve shorteningLagrangian mean curvature flowSingularities3-manifoldsStability & uniquenessLong-time existence & convergenceSasakian & contact geometry https://arxiv.org/abs/2210.12702arxiv:2210.12702Sun, 23 Oct 2022 00:00:00 GMTDer-Chen Chang, Shu-Cheng Chang, Yingbo Han, Chien Lin, Chin-Tung Wu — In this paper, we show that the uniform L^4-bound of the transverse Ricci curvature along the Sasaki-Ricci flow on a compact quasi-regular transverse Fano Sasakian (2n+1)-manifold M. When M is dimension up to seven and the space of leaves of the characteristic foliation is well-formed, we first show that any solution of the Sasaki-Ricci flow converges in the Cheeger-Gromov sense to the unique singular orbifold Sasaki-Ricci soliton on the limit space which is a S^1-orbibundle over the unique singular Kaehler-Ricci soliton on a normal projective variety with codimension two orbifold singularities. Secondly, for n=1, we show that there are only two nontrivial Sasaki-Ricci solitons on a compact quasi-regular Fano Sasakian three-sphere with its leave space a teardrop-like and football-like space, respectively. For n=2,3, we show that the Sasaki-Ricci soliton is trivial one if M is transverse K-stable.Ricci flowRicci solitonsKähler–Ricci solitonsSingularitiesKähler geometryKähler–Einstein & K-stabilitySasakian & contact geometry https://arxiv.org/abs/2203.00374arxiv:2203.00374Tue, 01 Mar 2022 00:00:00 GMTShu-Cheng Chang, Yingbo Han, Chien Lin, Chin-Tung Wu — In this paper, we show that the uniform L^4-bound of the transverse Ricci curvature along the Sasaki-Ricci flow on a compact quasi-regular Sasakian (2n+1)-manifold M of general type. As an application, any solution of the normalized Sasaki-Ricci flow converges in the Cheeger-Gromov sense to the unique singular Sasaki η-Einstein metric on the transverse canonical model M_can of M if n is less than or equal to 3. In particular for n equal to 2, M_can is a S^1-orbibundle over the unique Keahler-Einstein orbifold surface (Z_can,ω_KE) with finite point orbifold singularities. The floating foliation (-2)-curves in M will be contracted to orbifold points by the Sasaki-Ricci flow as t goes to infinite.Ricci flowEinstein metricsSingularitiesAnalytic minimal model programSasakian & contact geometry