本文研究具强负曲率Cartan－Hadamard流形M~n（n≥3）上给定数量曲率函数S的共形形变问题．利用上下解方法，并通过精心构造上解，我们获得了当完备的共形形变度量存在时，函数S在无穷远附近的最佳渐近性态．在较一般情况下，我们还给出了共形数量曲率方程解的渐近估计．

We study the conformal deformation for prescribing scalar curvature function S on Cartan-Hadamard manifold Mm (n 3) with strongly negative curvature.By employing the super-subsolution method and a careful construction for the supersolution, we obtain the best possible asymptotic behavior for S near infinity so thatthe problem of complete conformal deformal is solvable. In the more general cases,we prove an asymptotic estimation oil the solutions of the conformal scalar curvatureequation.