Dimension of polynomial growth harmonic functions on locally conformally flat manifolds with nonnegative Ricci curvature

Xiaohan Cai, Mijia Lai

Let ${\mathcal{H}}_d(M)$ denote the space of harmonic functions with polynomial growth of degree at most $d$ on a complete Riemannian manifold $(M,g)$. Yau raised two fundamental que…