Hyperbolic Yamabe problem

In this paper,we investigate the solutions of the hyperbolic Yamabe problem for the (1 + n)-dimensional Minkowski space-time.More precisely speaking,for the case of n =1,we derive a general solution of the hyperbolic Yamabe problem;for the case of n =2,3,we study the global existence and blowup phenomena of smooth solutions of the hyperbolic Yamabe problem;while for general multi-dimensional case n ≥ 2,we discuss the global existence and non-existence for a kind of exact solutions of the hyperbolic Yamabe problem.