We consider asymptotic behaviors of star-shaped curves expanding by $V=1-K$, where $V$ denotes the outward-normal velocity and $K$ curvature. In this paper, we show the followings. The difference of the radial functions between an expanding curve and circle has its asymptotic shape as $t\rightarrow+\infty$. For two curves, if the asymptotic shapes are identical, then the curves are also. The set of all asymptotic shapes is dense in $C(S^1)$.
"Asymptotic behaviors of star-shaped curves expanding by $V=1-K$." Differential Integral Equations 18 (2) 225 - 232, 2005.