Hyperbolic Yamabe problem

Abstract

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.