The Inverse Mean Curvature Flow Inside A Cone In Warped Products

The inverse mean curvature flow is proposed by physicists and is used to prove the Riemannian-Penrose inequality.After that,the inverse mean curvature flow is an impor-tant tool to prove geometric inequalities,which plays an important role in mathematical physics.In this paper,we consider the hypersurface in the warped product manifold which is orthonormal to a cone in warped product manifold,maintain it orthonomality along the evolution of inverse mean curvature flow.In this paper,we mainly study the long time existence of the inverse mean curvature flow and the asymptotic behavior of the surface under the evolution of the flow.