Study On The Singularity Of Non-local Area Preserving Flow

In this thesis,we study the evolution of area-preserving planar curve flow.For the case of embedded convex curve flow,three different methods are summarized to establish the uniform bound on curvature to prove the flow's convergence,including geometric estimate,support function method and energy functional method.For the case of immersed locally convex curve flow,we study the type of singularity and obtain the asymptotic behaviour of flow near singularity.