2011/09/05 by De-Xing Kong, Kong, De-Xing, Qiang Ru +1
Mathematics · #35M20 #53C21 #53C44 #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities #math.AP #msc:35M20 #msc:53C21 #msc:53C44
paper · pdf · doi:10.48550/arxiv.1109.0811
29 pages, 1 figure
arxiv created 2011/09/05 · openalex publication_date 2011/09/05 · arxiv updated 2011/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we introduce a new geometric flow with rotational invariance and prove that, under this kind of flow, an arbitrary smooth closed contractible hypersurface in the Euclidean space Rn+1 (n, 1) converges to Sn in the C1-topology as t goes to the infinity. This result covers the well-known theorem of Gage and Hamilton in [4] for the curvature flow of plane curves and the famous result of Huisken in [5] on the flow by mean curvature of convex surfaces, respectively.