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5. Singularities of the Curve Shortening Flow in a Riemannian Manifold

Singularities of the Curve Shortening Flow in a Riemannian Manifold

来源 :数学学报（英文版） | 被引量 : 0次 | 上传用户：okzhi

【摘 要】

：

In this paper,the curve shortening flow in a general Riemannian manifold is studied,Altschuler\'s results about the flow for space curves are generalized.For any n-dimensional(n≥2)Riemannian manifold(M,g)with some natural assumptions,we prove the planar

【作 者】

：

Shu Jing PAN 

【机 构】

：

School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,P.R.China

【出 处】

：

数学学报（英文版）

【发表日期】

：

2021年11期

【关键词】

：

Curve shortening flow blow-up singularity formation 

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论文部分内容阅读

In this paper,the curve shortening flow in a general Riemannian manifold is studied,Altschuler\'s results about the flow for space curves are generalized.For any n-dimensional(n≥2)Riemannian manifold(M,g)with some natural assumptions,we prove the planar phenomenon when the curve shortening flow blows up.

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