2023/04/19 by Shu-Cheng Chang, Chang, Shu-Cheng, Yingbo Han +3
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2306.03683
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 C3. 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.