ENERGY ESTIMATES AND LIOUVILLE THEOREMS FOR HARMONIC MAPS

2000 ◽  
Vol 11 (03) ◽  
pp. 413-448 ◽  
Author(s):  
MARCO RIGOLI ◽  
ALBERTO G. SETTI
Keyword(s):  
Vector Bundle ◽  
Riemannian Manifolds ◽  
Harmonic Maps ◽  
Energy Estimates ◽  
Liouville Type ◽  
Harmonic Forms ◽  
Liouville Theorems ◽  
Liouville Type Theorems

We obtain lower and upper energy estimates for harmonic maps between Riemannian manifolds under natural curvature conditions leading to various Liouville-type theorems. Some of the methods described may also be applied to vanishing-type problems for vector bundle-valued harmonic forms.

Liouville theorems for a class of fourth order elliptic equations

1980 ◽  
Vol 86 (1-2) ◽  
pp. 129-137 ◽  
Author(s):  
Vinod B. Goyal ◽  
Philip W. Schaefer
Keyword(s):  
Fourth Order ◽  
Elliptic Equations ◽  
Entire Solutions ◽  
Liouville Type ◽  
Liouville Theorems ◽  
Liouville Type Theorems ◽  
Solutions Of Equations ◽  
Fourth Order Elliptic Equations

SynopsisLiouville type theorems are obtained for bounded entire solutions of equations of the form Δ2u − q(x)Δu + p(x)u = 0 by means of subharmonic functionals and Green type inequalities.

scholarly journals Liouville type theorems for p-harmonic maps

2008 ◽  
Vol 342 (1) ◽  
pp. 354-360 ◽  
Author(s):  
Dong Joo Moon ◽  
Huili Liu ◽  
Seoung Dal Jung
Keyword(s):  
Harmonic Maps ◽  
Liouville Type ◽  
Liouville Type Theorems

Liouville Type Theorems in the Theory of Mappings of Complete Riemannian Manifolds

2017 ◽  
Vol 221 (6) ◽  
pp. 737-744
Author(s):  
I. A. Aleksandrova ◽  
J. Mikeš ◽  
S. E. Stepanov ◽  
I. I. Tsyganok
Keyword(s):  
Riemannian Manifolds ◽  
Liouville Type ◽  
Liouville Type Theorems ◽  
Complete Riemannian Manifolds
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