It was conjectured by Lang that a complex projective manifold is Kobayashi
hyperbolic if and only if it is of general type together with all of its
subvarieties. We verify this conjecture for projective manifolds whose
universal cover carries a bounded, strictly plurisubharmonic function. This
includes in particular compact free quotients of bounded domains.
Comment: 10 pages, no figures, comments are welcome. v3: following suggestions
made by the referee, the exposition has been improved all along the paper, we
added a variant of Theorem A which includes manifolds whose universal cover
admits a bounded psh function which is strictly psh just at one point, and we
added a section of examples. Final version, to appear on \'Epijournal G\'eom.
Alg\'ebrique