A NOTE ON THE MEAN CURVATURE FLOW IN RIEMANNIAN MANIFOLDS

Under the hypothesis of mean curvature flows of hypersurfaces, we prove that the limit of the smooth rescaling of the singularity is weakly convex. It is a generalization of the result due to G.Huisken and C. Sinestrari in. These apriori bounds are satisfied for mean convex hypersurfaces in locally symmetric Riemannian manifolds with nonnegative sectional curvature.     

紧致带边黎曼流形上度量的Ricci形变

Hamilton的Ricci流方法被广泛地应用于研究流形的几何和拓朴．利用Ricci流的方法,证明了对于任意一个具有全测地边界的n维紧致流形（n≥4）满足一定的拼挤条件可以形变为具有全测地边界的空间形式。