摘要
A smooth, compact and strictly convex hypersurface evolving in R^n＋1 along its mean curvature vector plus a forcing term in the direction of its position vector is studied in this paper. We show that the convexity is preserving as the case of mean curvature flow, and the evolving convex hypersurfaces may shrink to a point in finite time if the forcing term is small, or exist for all time and expand to infinity if it is large enough. The flow can converge to a round sphere if the forcing term satisfies suitable conditions which will be given in the paper. Long-time existence and convergence of normalization of the flow are also investigated.
A smooth, compact and strictly convex hypersurface evolving in R^n＋1 along its mean curvature vector plus a forcing term in the direction of its position vector is studied in this paper. We show that the convexity is preserving as the case of mean curvature flow, and the evolving convex hypersurfaces may shrink to a point in finite time if the forcing term is small, or exist for all time and expand to infinity if it is large enough. The flow can converge to a round sphere if the forcing term satisfies suitable conditions which will be given in the paper. Long-time existence and convergence of normalization of the flow are also investigated.
基金
supported by National Natural Science Foundation of China(Grant No.10971055)
Funds for Disciplines Leaders of Wuhan(Grant No.Z201051730002)
Project of Hubei Provincial Department of Education(Grant No.T200901)
supported by Fundao Ciênciae Tecnologia(FCT)through a doctoral fellowship SFRH/BD/60313/2009
