Harmonic functions of polynomial growth on complete manifolds

Author(s):  
Atsushi Kasue
Author(s):  
Bobo Hua

Abstract We study ancient solutions of polynomial growth to heat equations on graphs and extend Colding and Minicozzi’s theorem [9] 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.


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