Extremal bounded holomorphic functions and an embedding theorem for arithmetic varieties of rank \(\geq 2\) (Q706149)

We just list two of the several major results proved in this paper. Let \(\Omega\) be a bounded symmetric domain of rank \(\geq 2\), \(\Gamma \subset \Aut(\Omega )\) a torsion-free lattice, \(X:= \Omega /\Gamma\), \(D\) a bounded domain of a Stein manifold, \(G \subset \Aut(D)\) a torsion free group and \(f: X \to D/G\) a nonconstant holomorphic map and \(F: \Omega \to D\) its lifting to the universal covering spaces. Here the author proves that \(F\) is an embedding. Let \(Z\) be a normal complex space and \(g: X \to Z\) a proper surjective holomorphic map. Here the author proves that either \(g\) is an unramified covering map or \(\pi _1(Z)\) is finite.