4 papers
Evolution of hypersurfaces in -dimensional light-cone
Xinjie Jiang, Shengliang Pan, Yun Yang
In this paper, we investigate the evolutionary processes of hypersurfaces within half of the -dimensional light-cone. Depending on the evolutionary processes, our focus exte…
A fourth-order area-preserving curve flow in centro-equiaffine geometry
Xinjie Jiang, Shengliang Pan, Yanlong Zhang
In this paper, inspired by the work of Guan and Li (2015), we introduce a fourth-order centro-equiaffine invariant curve flow via the affine Minkowski formula. Without any smallnes…
Star-shaped Centrosymmetric Curves under Gage's Area-preserving Flow
Laiyuan Gao, Shengliang Pan
It is proved that Gage's area-preserving flow can evolve a centrosymmetric star-shaped initial curve smoothly, make it convex in a finite time and deform it into a circle as time t…
Evolving convex curves by a generalized length-preserving flow
Laiyuan Gao, Shengliang Pan
This paper deals with a generalized length-preserving flow for convex curves in the plane. It is shown that the flow exists globally and deforms convex curves into circles as time…