| In this thesis,we study the evolution of a curve flow in the plane,which can be regarded as the gradient flow of isoperimetric ratio,for immersed locally convex closed curves.In particular,it is shown that the flows starting from two classes of rotationally symmetric curves,i.e,highly symmetric curves and Abresch-Langer type curves,exist for all time and converge to m-fold circles as time goes to infinity. |
