Curve shortening flow in a 3-dimensional pseudohermitian manifold

被引：1

作者：

Pan, Shujing ^{[1
]}

Sun, Jun ^{[2
,3
]}

机构：

[1] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China

[2] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

[3] Wuhan Univ, Hubei Key Lab Computat Sci, Wuhan 430072, Peoples R China

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2021年 / 60卷 / 06期

关键词：

53C17; 53E50; DIFFERENTIAL GEOMETRY; SINGULARITIES;

D O I：

10.1007/s00526-021-02062-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce a curve shortening flow in a 3-dimensional pseudohermitian manifold with vanishing torsion. The flow preserves the Legendrian condition and decreases the length of curves. The stationary solution of our flow is a Legendrian geodesic. We classify the singularity and prove some convergence results. Moreover, we study the flow in Heisenberg group especially with Type I singularity.

引用

页数：23

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