Takeyuki Nagasawa, Kohei Nakamura. Source: Advances in Differential Equations, Volume 24, Number 9/10, 581--608.Abstract:
Several inequalities for the isoperimetric ratio for plane curves are derived. In particular, we obtain interpolation inequalities between the deviation of curvature and the isoperimetric ratio. As applications, we study the long-time behavior of some geometric flows of closed plane curves without a convexity assumption.