Theorem (uniformization). Let X be a compact Kahler manifold of dimension n with large, residually finite and nonamenable fundamental group. Then its universal covering is a bounded domain in the n-dimensional affine space.
Derived length of zero entropy groups acting on compact Kahler manifolds
Uniformization of klt pairs by bounded symmetric domains
The g-periodic subvarieties for an automorphism g of positive entropy on a compact Kahler manifold
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