科研之友
微信
新浪微博
Facebook
分享链接
摘要
We consider the Monge-Ampere-type equation det(A + lambda g) = const., where A is the Schouten tensor of a conformally related metric and lambda > 0 is a suitably chosen constant. When the scalar curvature is non-positive we give necessary and sufficient conditions for the existence of solutions. When the scalar curvature is positive and the first Betti number of the manifold is non-zero we also establish existence. Moreover, by adapting a construction of Schoen, we show that solutions are in general not unique.
- 出版日期2008
