A note on Lang's conjecture for quotients of bounded domains

TL;DR

This paper verifies Lang's conjecture for certain projective manifolds, specifically those with universal covers carrying bounded, strictly plurisubharmonic functions, including compact quotients of bounded domains.

Contribution

It proves Lang's conjecture for a class of projective manifolds with universal covers that admit bounded, strictly plurisubharmonic functions.

Findings

Lang's conjecture holds for manifolds with such universal covers

Includes compact free quotients of bounded domains as special cases

Advances understanding of hyperbolicity in complex geometry

Abstract

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.