how many "a"s can you find in:
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.
user
The passage contains thirty-five "a"s.
assistant