Generalized Liouville properties of manifolds
The authors announce several results published elsewhere on generalized Liouville theorems on manifolds. The main result is the following theorem proved in [\textit{T. H. Colding} and \textit{W. P. Minicozzi}, Ann. Math., II. Ser. 146, No. 3, 725-747 (1997)] which was conjectured by \textit{S. T. Yau} [Proc. Symp. Pure Math. 54, Part 1, 1-28 (1993; Zbl 0801.53001)]: For an open manifold with nonnegative Ricci curvature the space of harmonic functions with polynomial growth of a fixed rate is finite dimensional. This theorem is a consequence of a much more general result which is also presented in the paper.
scientific article; zbMATH DE number 991909