Harmonic functions of polynomial growth on complete manifolds

1993 ◽  
pp. 281-290 ◽  
Author(s):  
Atsushi Kasue
Keyword(s):  
Harmonic Functions ◽  
Polynomial Growth ◽  
Complete Manifolds

scholarly journals Dimensional Bounds for Ancient Caloric Functions on Graphs

2019 ◽  
Author(s):  
Bobo Hua
Keyword(s):  
Harmonic Functions ◽  
Polynomial Growth ◽  
Volume Growth ◽  
Heat Equations ◽  
Ancient Solutions

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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