scholarly journals A Liouville property for gradient graphs and a Bernstein problem for Hamiltonian stationary equations

2015 ◽  
Vol 150 (1-2) ◽  
pp. 151-157 ◽  
Author(s):  
Micah W. Warren
Keyword(s):  
Liouville Property ◽  
Bernstein Problem ◽  
Hamiltonian Stationary

scholarly journals The Bernstein Problem in Dimension 6

1996 ◽  
Vol 185 (2) ◽  
pp. 420-439 ◽  
Author(s):  
J.Carlos Gutierrez Fernandez
Keyword(s):  
Bernstein Problem

scholarly journals Solution of the Bernstein Problem in the Non-regular Case

2000 ◽  
Vol 223 (1) ◽  
pp. 109-132 ◽  
Author(s):  
J.Carlos Gutiérrez Fernández
Keyword(s):  
Regular Case ◽  
Bernstein Problem

scholarly journals Hamiltonian stationary Lagrangian fibrations

2019 ◽  
Vol 17 (3) ◽  
pp. 753-791
Author(s):  
Eveline Legendre ◽  
Yann Rollin
Keyword(s):  
Hamiltonian Stationary

scholarly journals A Bernstein problem in warped products

2016 ◽  
Vol 41 ◽  
pp. 699-704
Author(s):  
Juan A. Aledo ◽  
Rafael M. Rubio
Keyword(s):  
Warped Products ◽  
Bernstein Problem

Harmonic functions on ℝ-covered foliations

2009 ◽  
Vol 29 (4) ◽  
pp. 1141-1161
Author(s):  
S. FENLEY ◽  
R. FERES ◽  
K. PARWANI
Keyword(s):  
Harmonic Functions ◽  
Riemannian Metrics ◽  
Related Result ◽  
Continuous Functions ◽  
Property A ◽  
Liouville Property ◽  
Foliated Manifold ◽  
Curved Manifolds ◽  
Codimension One ◽  
Negatively Curved

AbstractLet (M,ℱ) be a compact codimension-one foliated manifold whose leaves are endowed with Riemannian metrics, and consider continuous functions on M that are harmonic along the leaves of ℱ. If every such function is constant on leaves, we say that (M,ℱ) has the Liouville property. Our main result is that codimension-one foliated bundles over compact negatively curved manifolds satisfy the Liouville property. A related result for ℝ-covered foliations is also established.

scholarly journals Amenability, Reiter's condition and Liouville property

2018 ◽  
Vol 274 (12) ◽  
pp. 3291-3324
Author(s):  
Cho-Ho Chu ◽  
Xin Li
Keyword(s):  
Liouville Property
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