Harmonic functions of polynomial growth on complete manifolds

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

Harmonic functions of polynomial growth on certain complete manifolds

1996 ◽  
Vol 6 (4) ◽  
pp. 619-627 ◽  
Author(s):  
Tanya Christiansen ◽  
Maciej Zworski
Keyword(s):  
Harmonic Functions ◽  
Polynomial Growth ◽  
Complete Manifolds

$p$-harmonic functions on complete manifolds with a weighted Poincaré inequality

2017 ◽  
Vol 40 (2) ◽  
pp. 343-357
Author(s):  
Bui Van Binh ◽  
Nguyen Thac Dung ◽  
Nguyen Thi Le Hai
Keyword(s):  
Harmonic Functions ◽  
Poincaré Inequality ◽  
Poincare Inequality ◽  
Weighted Poincaré Inequality ◽  
Complete Manifolds

scholarly journals Polynomial growth harmonic functions on finitely generated abelian groups

2013 ◽  
Vol 44 (4) ◽  
pp. 417-432 ◽  
Author(s):  
Bobo Hua ◽  
Jürgen Jost ◽  
Xianqing Li-Jost
Keyword(s):  
Harmonic Functions ◽  
Polynomial Growth ◽  
Abelian Groups ◽  
Finitely Generated

Positive Harmonic Functions on Complete Manifolds of Negative Curvature

1985 ◽  
Vol 121 (2) ◽  
pp. 429 ◽  
Author(s):  
Michael T. Anderson ◽  
Richard Schoen
Keyword(s):  
Harmonic Functions ◽  
Negative Curvature ◽  
Complete Manifolds ◽  
Positive Harmonic Functions

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.

scholarly journals Polynomial growth harmonic functions on groups of polynomial volume growth

2015 ◽  
Vol 280 (1-2) ◽  
pp. 551-567 ◽  
Author(s):  
Bobo Hua ◽  
Jürgen Jost
Keyword(s):  
Harmonic Functions ◽  
Polynomial Growth ◽  
Volume Growth
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