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Peter Li, Luen-Fai Tam, Positive Harmonic Functions on Complete Manifolds with Non-Negative Curvature Outside a Compact Set, Annals of Mathematics, Vol. 125, No. 1 (Jan., 1987), pp. 171-207 ...
Michael T. Anderson, Richard Schoen, Positive Harmonic Functions on Complete Manifolds of Negative Curvature, Annals of Mathematics, Vol. 121, No. 2 (Mar., 1985), pp ...