Pinching Estimation For A Class Of Curvature Flow

In this paper,we study the curvature flow equation(?)X(x,t)=?(?)of hypersurfaces in Euclidean space under the condition of k=2.We use the first basic form and the second basic form of the evolution equation and the maximum principle to get the pinching estima-tion of the curvature flow.For the curvature flow equation(?)X(x,t)=(?).whenk=1.it represents the mean curvature flow;when k=n,it represents the Gauss curvature flow,and n is the unit normal vector.Referring to the pinching estimation of the mean curvature flow,we get the pinching estimation of the curvature flow equation(?)X(x,t)=(?)in the case of k=2.The first part of the article introduces the basic knowledge needed for curvature flow and the discussion of curvature flow,and gives the development equation of the geometric quantity of the mean curvature flow with time.The second part gives and proves the evolu?tion equation of the geometric quantity with time under the equation(?)X(x,t)=R1/2n;the third part of the use of these equations to obtain the development of curvature flow pinching estimate.