**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.

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