Singularities of the area preserving curve shortening flow with a free boundary condition

2018 ◽  
Vol 371 (3-4) ◽  
pp. 1429-1448 ◽  
Author(s):  
Elena Mäder-Baumdicker
Keyword(s):  
Boundary Condition ◽  
Free Boundary ◽  
Free Boundary Condition ◽  
Curve Shortening Flow ◽  
Curve Shortening ◽  
Area Preserving

scholarly journals The area preserving curve shortening flow with Neumann free boundary conditions

2015 ◽  
Vol 1 (1) ◽  
Author(s):  
Elena Mäder-Baumdicker
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Convex Domain ◽  
Euclidean Plane ◽  
Initial Curve ◽  
Curve Shortening Flow ◽  
Free Boundary Conditions ◽  
Curve Shortening ◽  
The Given ◽  
Area Preserving

AbstractWe study the area preserving curve shortening flow with Neumann free boundary conditions outside of a convex domain in the Euclidean plane. Under certain conditions on the initial curve the flow does not develop any singularity, and it subconverges smoothly to an arc of a circle sitting outside of the given fixed domain and enclosing the same area as the initial curve.

scholarly journals SUPERSYMMETRIC WZW σ MODEL ON INFINITE AND HALF-PLANE

2005 ◽  
Vol 20 (13) ◽  
pp. 2763-2772
Author(s):  
R. A. ZAIT ◽  
M. F. MOURAD
Keyword(s):  
Boundary Condition ◽  
Free Boundary ◽  
Half Plane ◽  
Infinite Number ◽  
Equations Of Motion ◽  
Free Boundary Condition ◽  
Infinite Plane ◽  
Recursion Relations ◽  
Conserved Currents

We study classical integrability of the supersymmetric U(N) σ model with the Wess–Zumino–Witten term on infinite and half-plane. We demonstrate the existence of nonlocal conserved currents of the model and derive general recursion relations for the infinite number of the corresponding charges in a superfield framework. The explicit forms of the first few supersymmetric charges are constructed. We show that the considered model is integrable on infinite plane as a consequence of the conservation of the supersymmetric charges. Also, we study the model on half-plane with free boundary, and examine the conservation of the supersymmetric charges on half-plane and find that they are conserved as a result of the equations of motion and the free boundary condition. As a result, the model on half-plane with free boundary is integrable. Finally, we conclude the paper and some features and comments are presented.

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