The blow-up of the conformal mean curvature flow

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2020,（4）
• 页码范围: 733-754
• 页数: 22页
• 语种: 英文

摘要

In this paper,we introduce and study the conformal mean curvature flow of submanifolds of higher codimension in the Euclidean space Rn.This kind of flow is a special case of a general modified mean curvature flow which is of various origination.As the main result,we prove a blow-up theorem concluding that,under the conformal mean curvature flow in Rn,the maximum of the square norm of the second fundamental form of any compact submanifold tends to infinity in finite time.Furthermore,we also prove that the external conformal forced mean curvature flow of a compact submanifold in Rn with the same pinched condition as Andrews-Baker's will be convergent to a round point in finite time.