We present an alternative proof of the uniform and Hausdorff exponential convergence results for Michael Gage's area-preserving curve shortening flow (APCSF) using Leon Simon's framework based on Łojasiewicz-Simon inequalities. We introduce a functional that combines length and area on $L^2(\mathbb S^1)$ and establish the optimal Łojasiewicz-Simon inequality for it to achieve the desired convergence.
(석사논문심사)
