In this note,we generalize an extension theorem in [Le-Sesum] and [Xu-Ye-Zhao] of the mean curvature flow to the Hk mean curvature flow under some extra conditions.The main difficulty in proving the extension theorem ...In this note,we generalize an extension theorem in [Le-Sesum] and [Xu-Ye-Zhao] of the mean curvature flow to the Hk mean curvature flow under some extra conditions.The main difficulty in proving the extension theorem is to find a suitable version of Michael-Simon inequality for the Hk mean curvature flow,and to do a suitable Moser iteration process.These two problems are overcome by imposing some extra conditions which may be weakened or removed in our forthcoming paper.On the other hand,we derive some estimates for the generalized mean curvature flow,which have their own interesting.展开更多
A Finsler metric on a manifold M with its flag curvature K is said to be almost isotropic flag curvature if K = 3c ＋ δ where δ and c are scalar functions on M. In this paper, we establish the intrinsic relation bet...A Finsler metric on a manifold M with its flag curvature K is said to be almost isotropic flag curvature if K = 3c ＋ δ where δ and c are scalar functions on M. In this paper, we establish the intrinsic relation between scalar functions c（x） and a（x）. More general, by invoking the Ricci identities for a one form, we investigate Finsler metric of weakly isotropic flag curvature K = 3θ/F ＋ δ and show that F has constant flag curvature if θ is horizontally parallel.展开更多
文摘In this note,we generalize an extension theorem in [Le-Sesum] and [Xu-Ye-Zhao] of the mean curvature flow to the Hk mean curvature flow under some extra conditions.The main difficulty in proving the extension theorem is to find a suitable version of Michael-Simon inequality for the Hk mean curvature flow,and to do a suitable Moser iteration process.These two problems are overcome by imposing some extra conditions which may be weakened or removed in our forthcoming paper.On the other hand,we derive some estimates for the generalized mean curvature flow,which have their own interesting.
基金Supported by the National Natural Science Foundation of China(11071005)Research Fund for the Doctoral Program of Higher Education of China 20110001110069
文摘A Finsler metric on a manifold M with its flag curvature K is said to be almost isotropic flag curvature if K = 3c ＋ δ where δ and c are scalar functions on M. In this paper, we establish the intrinsic relation between scalar functions c（x） and a（x）. More general, by invoking the Ricci identities for a one form, we investigate Finsler metric of weakly isotropic flag curvature K = 3θ/F ＋ δ and show that F has constant flag curvature if θ is horizontally parallel.
