UBC Mathematics Department
http://www.math.ubc.ca

Colloquium Abstract: Professor Peter Li, Department of Mathematics, University of California, Irvine

Polynomial growth harmonic functions on complete manifolds

In this talk, I will give a brief survey and some recent results on the understanding of the dimension of the space of harmonic functions that grows at most polynomially of degree d. If the manifold is Euclidean space, our setting includes solutions of any 2nd order, uniformly bounded, elliptic operator with measurable coefficients of either divergence or non-divergence form. On the other hand, it also includes harmonic (holomorphic) sections of a (holomorphic) vector bundle over a complete Riemannian manifold with non-negative Ricci curvature.