Harmonic functions of linear growth on Kähler manifolds with nonnegative Ricci curvature (Q1902203)

The main result of this paper asserts that the space \(H^1 (M)\) of harmonic functions of linear growth on a complete Kähler manifold \(M\) with nonnegative Ricci curvature satisfies \[ \dim H^1 (M)\leq 2\dim_\mathbb{C} M+1, \] and equality holds iff \(M\) is isometric to \(\mathbb{C}^m\) with standard flat metric.