Ella Wilson will give a talk on 03/18/2025.

In the 1970s, Yau conjectured that for open manifolds with nonnegative Ricci curvature, the space of harmonic functions with polynomial growth of a fixed rate is finite dimensional. In this talk we will cover Colding and Minnicozzi’s 1997 Annals paper in which they prove this conjecture for a larger class of manifolds, namely complete Riemannian manifolds that satisfy a doubling property and a uniform Poincaré-type inequality. We will also discuss applications of this result to area-minimizing hypersurfaces in Euclidean space.