Abstract
In this paper, we prove a general stability result for higher-order geometric flows on the circle, which basically states that if the initial condition is close to a round circle, the curve evolves smoothly and exponentially fast towards a circle (possibly not the one it started close to), and we improve on known convergence rates (which we believe are almost sharp). The polyharmonic flow is an instance of the flows to which our result can be applied. We will also present general families of flows for which our stability result applies.
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