Dimensional bounds for ancient caloric functions on graphs

10 Mar 2019 · Hua Bobo ·

We study ancient solutions of polynomial growth to heat equations on graphs, and extend Colding and Minicozzi's theorem [CM19] on manifolds to graphs: For a graph of polynomial volume growth, the dimension of the space of ancient solutions of polynomial growth is bounded by the product of the growth degree and the dimension of harmonic functions with the same growth.