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

I. A. Aleksandrova; J. Mikeš; S. E. Stepanov; I. I. Tsyganok

doi:10.1007/s10958-017-3262-2

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

Journal of Mathematical Sciences ◽

10.1007/s10958-017-3262-2 ◽

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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Liouville-Type Theorems and Applications to Geometry on Complete Riemannian Manifolds

Journal of Geometric Analysis ◽

10.1007/s12220-011-9239-3 ◽

2011 ◽

Vol 23 (1) ◽

pp. 96-105 ◽

Cited By ~ 2

Author(s):

Chanyoung Sung

Keyword(s):

Riemannian Manifolds ◽

Liouville Type ◽

Liouville Type Theorems ◽

Complete Riemannian Manifolds

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Gradient estimates and Liouville type theorems for $$(p-1)^{p-1}\Delta _pu+au^{p-1}\log u^{p-1}=0$$ on Riemannian manifolds

Archiv der Mathematik ◽

10.1007/s00013-021-01639-4 ◽

2021 ◽

Author(s):

Bingqing Ma ◽

Mingfang Zhu

Keyword(s):

Riemannian Manifolds ◽

Gradient Estimates ◽

Liouville Type ◽

Liouville Type Theorems

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Liouville-type theorems for biharmonic maps between Riemannian manifolds

Advances in Calculus of Variations ◽

10.1515/acv.2010.003 ◽

2010 ◽

Vol 3 (1) ◽

Cited By ~ 19

Author(s):

Paul Baird ◽

Ali Fardoun ◽

Seddik Ouakkas

Keyword(s):

Riemannian Manifolds ◽

Biharmonic Maps ◽

Liouville Type ◽

Liouville Type Theorems

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A Liouville-type theorem for biharmonic maps between complete Riemannian manifolds with small energies

Archiv der Mathematik ◽

10.1007/s00013-018-1189-6 ◽

2018 ◽

Vol 111 (3) ◽

pp. 329-336 ◽

Cited By ~ 6

Author(s):

Volker Branding

Keyword(s):

Riemannian Manifolds ◽

Type Theorem ◽

Biharmonic Maps ◽

Liouville Type ◽

Liouville Type Theorem ◽

Complete Riemannian Manifolds

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Liouville-type theorems for CC-harmonic maps from Riemannian manifolds to pseudo-Hermitian manifolds

Annals of Global Analysis and Geometry ◽

10.1007/s10455-017-9547-3 ◽

2017 ◽

Vol 52 (1) ◽

pp. 25-44

Author(s):

Tian Chong ◽

Yuxin Dong ◽

Yibin Ren

Keyword(s):

Riemannian Manifolds ◽

Harmonic Maps ◽

Liouville Type ◽

Hermitian Manifolds ◽

Liouville Type Theorems

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Some Liouville-type Theorems for the Stationary Ginsburg – Landau Equation on Quasi-model Riemannian Manifolds

Izvestiya of Saratov University New Series Series Mathematics Mechanics Informatics ◽

10.18500/1816-9791-2015-15-2-127-135 ◽

2015 ◽

Vol 15 (2) ◽

pp. 127-135 ◽

Cited By ~ 1

Author(s):

S.S. Vikharev ◽

Keyword(s):

Riemannian Manifolds ◽

Landau Equation ◽

Liouville Type ◽

Liouville Type Theorems

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Liouville type theorems for systems of elliptic differential inequalities on Riemannian manifolds

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2018.05.084 ◽

2018 ◽

Vol 466 (1) ◽

pp. 426-446

Author(s):

Fanheng Xu ◽

Lifei Wang ◽

Yuhua Sun

Keyword(s):

Riemannian Manifolds ◽

Differential Inequalities ◽

Liouville Type ◽

Liouville Type Theorems

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Liouville-type theorems for some classes of Riemannian almost product manifolds and for special mappings of Riemannian manifolds

Differential Geometry and its Applications ◽

10.1016/j.difgeo.2017.03.006 ◽

2017 ◽

Vol 54 ◽

pp. 111-121 ◽

Cited By ~ 1

Author(s):

Sergey E. Stepanov ◽

Josef Mikeš

Keyword(s):

Riemannian Manifolds ◽

Liouville Type ◽

Liouville Type Theorems

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A Liouville-type result for quasi-linear elliptic equations on complete Riemannian manifolds

Journal of Functional Analysis ◽

10.1016/j.jfa.2004.05.009 ◽

2005 ◽

Vol 219 (2) ◽

pp. 400-432 ◽

Cited By ~ 15

Author(s):

Stefano Pigola ◽

Marco Rigoli ◽

Alberto G. Setti

Keyword(s):

Riemannian Manifolds ◽

Elliptic Equations ◽

Type Result ◽

Liouville Type ◽

Complete Riemannian Manifolds

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ENERGY ESTIMATES AND LIOUVILLE THEOREMS FOR HARMONIC MAPS

International Journal of Mathematics ◽

10.1142/s0129167x00000211 ◽

2000 ◽

Vol 11 (03) ◽

pp. 413-448 ◽

Cited By ~ 4

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.

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