Stability of the Shrinking Semi-Circle Under the Free Boundary Curve Shortening Flow

For a free boundary curve shortening flow in a convex domain whose maximal time of existence is finite, we prove that \[\frac{R(\Gamma_{t} - p)}{\sqrt{2(T-t)}} \to S^{1}_{+},\] at a rate no slower than \((T-t)^{1-\delta}\) for any \(\delta > 0\).

Recommended citation: Theodora Bourni, Nathan Burns and Mat Langford (2026). "Stability of the Shrinking Semi-Circle under the Free Boundary Curve Shortening Flow" arXiv:2603.06949.
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