scholarly journals Linear growth harmonic functions on complete manifolds

1995 ◽  
Vol 3 (4) ◽  
pp. 683-698 ◽  
Author(s):  
Jiaping Wang
Keyword(s):  
Harmonic Functions ◽  
Linear 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

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 Harmonic functions of linear growth on solvable groups

2016 ◽  
Vol 216 (1) ◽  
pp. 149-180 ◽  
Author(s):  
Tom Meyerovitch ◽  
Ariel Yadin
Keyword(s):  
Harmonic Functions ◽  
Linear Growth ◽  
Solvable Groups

scholarly journals Existence and non-existence of minimal graphic and p-harmonic functions

2019 ◽  
Vol 150 (1) ◽  
pp. 341-366
Author(s):  
Jean-Baptiste Casteras ◽  
Esko Heinonen ◽  
Ilkka Holopainen
Keyword(s):  
Harmonic Functions ◽  
Linear Growth ◽  
Entire Solution ◽  
Complete Riemannian Manifold ◽  
The Other ◽  
Hadamard Manifolds ◽  
Minimal Graph ◽  
Rotationally Symmetric ◽  
Sectional Curvatures ◽  
Negative Sectional Curvature

AbstractWe prove that every entire solution of the minimal graph equation that is bounded from below and has at most linear growth must be constant on a complete Riemannian manifold M with only one end if M has asymptotically non-negative sectional curvature. On the other hand, we prove the existence of bounded non-constant minimal graphic and p-harmonic functions on rotationally symmetric Cartan-Hadamard manifolds under optimal assumptions on the sectional curvatures.

scholarly journals Infinity Harmonic Functions over Exterior Domains

2020 ◽  
Author(s):  
Guanghao Hong ◽  
Yizhen Zhao
Keyword(s):  
Growth Rate ◽  
Harmonic Functions ◽  
Linear Growth ◽  
Linear Growth Rate ◽  
Dirichlet Problems ◽  
Exterior Domains

Abstract In this paper, we study the infinity harmonic functions with linear growth rate at infinity defined on exterior domains. We show that such functions must be asymptotic to planes or cones at infinity. We also establish the solvability of Dirichlet problems for exterior domains.

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