• Corpus ID: 119121821

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… 

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