A Class Of Inverse Mean Curvature Flow In Rⁿ⁺¹

This paper mainly studies a class of inverse curvature flow with distance function in Euclidean space,?_tX=1/(f(|X|)H)ν,where X is the coordinate vector of the hypersurface in Euclidean space,H is the mean curvature of the hypersurface,νis the unit outer normal vector of the hypersurface;when the initial hypersurface is compact,boundless,mean convex,star-shaped,the solution of the curvature flow has a long-time existence and converges to a spherical surface in Euclidean space after proper rescaling.This paper first introduces the basic knowledge needed for the study:the basic formula of submanifold geometry,the maximum principle on compact manifold,the evolution equation of the second basic form,which is used to estimate C~0,C~1,C~2,combined with the basic knowledge of the parabolic equation to get the long-time existence of the curvature flow,and finally the initial hypersurface converges to a spherical surface in Euclidean space after proper rescaling.