Global Curvature Estimation For The Solutions Of A Class Of Hessian Type Prescribed Curvature Equations

In this paper,we mainly study the curvature estimates of the solution of prescribed curvature equation in the following forms:?_k???X?+b?X??=??X,??,X?M.?0.1?Where M?Rⁿ⁺¹is an n-dimensional closed hypersurface.Suppose X,?represent the point on surface M and the normal vector outside the unit of the point.Suppose?_kis k-elementary symmetric function.Let??X?is the principal curvature at point X.b?X?is some given smooth symmetric 2-tensor.??X,??>0 is a given smooth function.In this paper,we mainly discuss the curvature estimation of the prescribed curvature e-quation?0.1?.For general?^1/k?X,??>0,the curvature estimation of k+1convex solution of equation?0.1?is established.Namely,when??X???_n,b?X???_k+1,the curvature of the equation?0.1?has a priori upper bound.