Entropy Of Curves Flow

Curve flow is using the geometry and the analysis method to study how curve developing accord to certain way. In the past several decades, emergencing of a large number of literatures to discuss the development of the curve.The entropy of the solutions of heat equation provides another powerful tool to study the curve flow, it as the research development and change of the flow curve provides another important method, aroused the interest of many scholars.First chapter is the introduction part briefly introduces the research background of curve flow’s entropy and the status quo, some of the basic knowledge and basic formula of the thesis are given.The second chapter mainly introduces plane curve flow ( ) [ ] [ )2r u,t: a,b ′0,+￥ ®R, ( ) ( )0r u,0 =r u and meet the heat equationsome of the basic formula of the flow curve is deduced.The fourth chapter deduces a derivative( ( ) ( )22logse￠t == -k é ?k -k ùds? ?ò) of the entropy( e(t)= òklogkds) and second derivative( ( ) ( )22 22 logse￠t =k ?k +k dsò).The fifth chapter introduces heat equation(uuand its entropy( ( ) log duMt =u u p mòN).The entropy formula are discussed under compact manifold and noncompact manifold, and gives some interesting results.The sixth chapter This chapter independently of the front content, through direct calculation,get the development equation of the mean curvature flow in the Ricci flow.