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

## Elena Mäder-Baumdicker

created by paolini on 13 Jun 2014

19 jun 2014 -- 14:35   [open in google calendar]

Abstract.

Under the area preserving curve shortening flow (APCSF), a convex simple closed plane curve converges smoothly to a circle with the same enclosed area as the initial curve (due to Gage). Note that this limit curve is the solution of the isoperimetric problem in R2. Corresponding to the outer isoperimetric problem for a convex domain we study the APCSF with Neumann free boundary conditions outside of a convex domain. Under certain conditions on the initial curve the flow does not develop any singularity, and it converges smoothly to an arc of a circle sitting outside of the given convex domain and enclosing the same area as the initial curve.

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