Abstract
We show that for embedded or convex plane curves expansion, the difference u(x,t)-r(t) in support functions between the expanding curves γ <sub>t</sub> and some expanding circles C <sub>t</sub> (with radius r(t)) has its asymptotic shape as t→∞. Moreover the isoperimetric difference L <sup>2</sup> -4πA is decreasing and it converges to a constant script S sign > 0 if the expansion speed is asymptotically a constant and the initial curve is not a circle. For convex initial curves, if the expansion speed is asymptotically infinite, then L <sup>2</sup> -4πA decreases to script S sign = 0 and there exists an asymptotic center of expansion for γ <sub>t</sub> . © Springer-Verlag 2005.