CH流形上的方程△u-hu+fu^p=0与黎曼度量的共形形变

On the Equation △u-hu+fu^p=0 and ConformalDeformations of Riemannian Metrics on CH Manifolds

设 M是一个度量 g的完备非紧非正曲率单连通黎曼流形 ,k是它的数曲率 ,K是 M上的光滑函数 .作者给出了 M上以 K作为数曲率且共形于 g的度量的存在性条件 ,并给出了方程△ u- hu+fup

Let M be a complete noncompact simply-connected Rie mannian manifold of nonpositive curvature with metric g, k its scalar curvat ure, and K a C\+∞ function on M. The author gives some conditions u nder which there exist other complete metrics on M conformal to g with K as their scalar curvature, and obtains some existence results of positive solutions of the equation △u-hu+fu\+p=0 on M.