Curve shortening flow in a 3-dimensional pseudohermitian manifold

Curve shortening flow in a 3-dimensional pseudohermitian manifold

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...

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Veröffentlicht in:Calculus of variations and partial differential equations 2021-12, Vol.60 (6), Article 212
Hauptverfasser: Pan, Shujing, Sun, Jun
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Calculus of Variations and Optimal Control
Optimization
Control
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Singularities
Systems Theory
Theoretical
Three dimensional flow
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Zusammenfassung: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.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-021-02062-x