https://neckpinch.com/authors/chin-tung-wu/New arXiv papers by Chin-Tung Wu, 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/2406.16430arxiv:2406.16430Mon, 24 Jun 2024 00:00:00 GMTShu-Cheng Chang, Fengjiang Li, Chien Lin, Chin-Tung Wu — In this paper, we derive the uniform L^4-bound of the transverse conic Ricci curvature along the conic Sasaki-Ricci flow on a compact transverse log Fano Sasakian manifold M of dimension five and the space of leaves of the characteristic foliation is not well-formed. Then we first show that any solution of the conic Sasaki-Ricci flow converges in the Cheeger-Gromov sense to the unique singular orbifold conic Sasaki-Ricci soliton on M_infinite which is a S^1-orbibundle over the unique singular conic Keahler-Ricci soliton on a log del Pezzo orbifold surface. As a consequence, there exists a Keahler-Ricci soliton orbifold metric on its leave space which is a log del Pezzo orbifold surface. Second, we show that the conic Sasaki-Ricci soliton is the conic Sasaki-Einstein if M is transverse log K-polystable. In summary, we have the existence theorems of orbifold Sasaki-Ricci solitons and Sasaki-Einstein metrics on a compact quasi-regular Sasakian manifold of dimension five.Ricci flowRicci solitonsEinstein metricsKähler geometryKähler–Einstein & K-stabilitySasakian & contact geometry https://arxiv.org/abs/2312.15996arxiv:2312.15996Tue, 26 Dec 2023 00:00:00 GMTShu-Cheng Chang, Chin-Tung Wu, Liuyang Zhang — In this article, we recapture the Smale conjecture on a Sasakian 3-sphere via the Legendrian mean curvature flow. More precisely, we deform the area-preserving contactomorphism (symplectomorphism) of Sasakian 3-spheres to an isometry via the Legendrian mean curvature flow on the Legendrian graph in S²× S³. By using the monotonicity formula and blow-up analysis, we obtain the minimal Legendrian graph in S²× S³. Finally, we will address the rigidity theorem of 2-dimensional Legendrian self-shrinkers in ℝ⁵. We are able to reconstruct the Harvey-Lawson special Lagrangian cone in ℂ³ from this Legendrian self-shrinker. The partial classification is also provided if the squared norm of the second fundamental form is constant.Mean curvature flowLagrangian mean curvature flowSelf-shrinkers & translatorsSingularitiesSmale conjecture & diffeomorphismsStability & uniquenessSasakian & 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/2203.01736arxiv:2203.01736Thu, 03 Mar 2022 00:00:00 GMTShu-Cheng Chang, Chien Lin, Chin-Tung Wu — Let (M,η,ξ,Φ,g) be a compact quasi-regular Sasakian 5-manifold with finite cyclic quotient foliation singularities of type (1/r)(1,a). First, we derive the foliation minimal model program by applying the resolution of cyclic quotient foliation singularities. Secondly, based on the study of local model of resolution of foliation singularities, we prove the foliation canonical surgical contraction or the foliation extremal ray contraction under the Sasaki-Ricci flow. As a consequence, we prove a Sasaki analogue of analytic minimal model program with the Keahler-Ricci flow due to Song-Tian and Song-Weinkove.Ricci flowSingularitiesAnalytic minimal model programSasakian & 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