# The area preserving curve shortening flow with Neumann free boundary conditions

@inproceedings{MaderBaumdicker2014TheAP, title={The area preserving curve shortening flow with Neumann free boundary conditions}, author={Elena Mader-Baumdicker}, year={2014} }

κ ds L ≕ κ̄ is the average of the curvature. For simple closed curves ̄ κ = 2π L holds. Gage pointed out that this evolution equation arises as the “ L2-gradient flow” of the length functional under the constant enclosed area constraint. The term ̄ κ is the suitable Lagrange parameter for this variational problem. Gage proved that a strictly convex simple closed cu rve which evolves according to (1) remains strictly convex and converges to a circle in the C∞ metric ast → ∞, see [15, Theorem 4.1…

## 5 Citations

Constrained Curve Flows

- Mathematics
- 2018

In this thesis we consider closed, embedded, smooth curves in the plane whose local total curvature does not lie below −π and study their behaviour under the area preserving curve shortening flow…

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

- Mathematics
- 2017

We consider the area preserving curve shortening flow with Neumann free boundary conditions outside of a convex domain or at a straight line. We give a criterion on initial curves that guarantees the…

Evolution of locally convex closed curves in the area-preserving and length-preserving curvature flows

- Mathematics
- 2020

We provide sufficient conditions on an initial curve for the area preserving and the length preserving curvature flows of curves in a plane, to develop a singularity at some finite time or converge…

The area preserving curve shortening flow with Neumann free boundary conditions

- Mathematics
- 2015

Abstract We 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…

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The area preserving curve shortening flow with Neumann free boundary conditions

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Abstract We 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…

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