具有平衡项的平均曲率流

Mean curvature flow with a forcing term

讨论具有一般平衡项的平均曲率流.如果平衡项有上界,平均曲率流的第一型奇异点是自相似的,而且,如果平衡项的上界足够小,具有此平衡项的凸平均曲率流和一般平均曲率流有相同的性质.

Mean curvature flow of compact hypersurfaces with a forcing term was studied in this paper.It was showed that the forced mean curvature flow of Type I singularity was self-similar if the forcing term was bounded from above.Moreover,if the upper bound of the forcing term was small enough,we proved that such convex forced mean curvature flow had the same property as that of the well-known mean curvature flow.