Bounded harmonic functions on Riemannian manifolds of nonpositive curvature

摘要

Certain general conditions are put forth on a complete simply-connected Riemannian manifold of nonpositive curvature which guarantee that they support nontrivial bounded harmonic functions. This result includes the Cartan-Hadamard manifolds with curvature pinched between two negative constants and the bounded symmetric domains R _I(n, n) and R _(II)(n) (n ≥ 2) as special cases.