Legendrian mean curvature flow in $\eta$-Einstein Sasakian manifolds
Abstract
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 {\eta}-Einstein Sasakian (2n+1)-manifolds under the suitable stability condition due to the Thomas-Yau conjecture.
Keywords
Cite
@article{arxiv.2306.03683,
title = {Legendrian mean curvature flow in $\eta$-Einstein Sasakian manifolds},
author = {Shu-Cheng Chang and Yingbo Han and Chin-Tung Wu},
journal= {arXiv preprint arXiv:2306.03683},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:0906.5527 by other authors