Harmonic functions and the structure of complete manifolds (Q1203616)

Let \(M\) be a complete manifold without boundary. As known, if the sectional curvature of \(M\) is nonnegative outside some compact subset of \(M\), then \(M\) has finite topological type. In particular, \(M\) has finitely many ends. In a previous paper, the authors established the relation between the numbers of the ends and the dimensions of the spaces of all bounded harmonic functions and all positive harmonic functions on \(M\). This paper shows a more general version of the above results, under a weakened assumption on Ricci curvature. Some applications to Riemannian geometry and Kaehler geometry are given too.