AbstractSelf-expanders are a special class of solutions to the mean curvature flow, in which a later time slice is a scale-up copy of an earlier one. They are also critical points for a suitable weighted area functional. Self-expanders model the asymptotic behavior of a mean curvature flow when it emerges from a cone singularity. The nonuniqueness of self-expanders presents challenges in the st...
AbstractAt first, l will review some basic knowledge of Gz geometry. Then, l will introduce the LaplacianGz flow and review some results about its long time existence. Lastly, l wil talk about our resultabout the long time existence of the Laplacian Gz flow with bounded scalar curvature and Cl normof Weyl tensor. This talk is based on a joint work with Professor Yi Li