2015/04/09 by Qing-Ming Cheng, Cheng, Qing-Ming, Shiho Ogata +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1504.02225
openalex publication_date 2015/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is our purpose to study complete self-shrinkers in Euclidean space. First of all, we show some examples of complete self-shrinkers without polynomial volume growth. By making use of the generalized maximum principle for L-operator, we give a complete classification for 2-dimensional complete self-shrinkers with constant squared norm of the second fundamental form in \mathbb R3. In \citeDX2, Ding and Xin have proved this result under the assumption of polynomial volume growth, which is removed in our theorem.