On the Martin boundary of Riemannian products (Q756159)

Let \(X=X_ 1\times X_ 2\) be the Riemannian product of two complete, non-compact Riemannian manifolds with Ricci curvature bounded from below. The author shows that a function f on X is a minimal positive harmonic function iff it is the product \(f=f_ 1f_ 2\) of minimal positive \(\lambda_ i\)-eigenfunctions \(f_ i\) on \(X_ i\) with \(\lambda_ 1+\lambda_ 2=0\).