Yau's finite-dimensionality conjecture for polynomial-growth harmonic functions

Let $M$ be a complete noncompact (open) Riemannian manifold with nonnegative Ricci curvature. For a fixed growth rate, consider the vector space of harmonic functions on $M$ with polynomial growth of that rate. Yau's conjecture. This space is finite dimensional. This conjecture generalizes the corresponding Euclidean result and concerns the structure of harmonic functions on manifolds with nonnegative Ricci curvature; its resolution is not specified in the source.