https://neckpinch.com/authors/chien-lin/New arXiv papers by Chien Lin, 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/2502.16148arxiv:2502.16148Sat, 22 Feb 2025 00:00:00 GMTShu-Cheng Chang, Fengjiang Li, Chien Lin, Hongbing Qiu — In this paper, we study several properties of Sasaki-Ricci solitons as singularity models of the Sasaki-Ricci flow. First, we establish several fundamental equations for Sasaki-Ricci solitons, which enable us to derive potential estimates and prove the positivity of the scalar curvature. Then we present two criteria for the transverse rigidity of Sasaki-Ricci solitons. As essential applications, we prove that any low-dimensional Sasaki-Ricci soliton with constant scalar curvature must be Sasaki-Einstein, and that any Sasaki-Ricci soliton with harmonic Weyl tensor is a finite quotient of the sphere.Ricci flowRicci solitonsSingularitiesScalar curvatureStability & uniquenessSasakian & 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/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