Add to ORKGLet (M,F) be a compact codimension-one foliated manifold whose leaves are equipped 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. Related results for R-covered foliations, as well as for discrete group actions and discrete harmonic functions, are also established
AbstractFor each n ⩾ 3, we present a family of Riemannian metrics g on Rn such that each Riemannian ...
We prove several Liouville theorems for harmonic maps between certain classes of Riemannian manifold...
In this paper, we prove two Liouville theorems for harmonic maps and apply them to study the topolog...
Let (M,F) be a compact codimension-one foliated manifold whose leaves are equipped with Riemannian m...
Let (M,F) be a compact codimension-one foliated manifold whose leaves are equipped with Riemannian m...
Let (M,F) be a compact codimension-one foliated manifold whose leaves are equipped with Riemannian m...
Let (M,F) be a compact codimension-one foliated manifold whose leaves are equipped with Riemannian m...
AbstractBy using probabilistic approaches, Liouville theorems are proved for a class of Riemannian m...
AbstractBy using probabilistic approaches, Liouville theorems are proved for a class of Riemannian m...
By using probabilistic approaches, Liouville theorems are proved for a class of Riemannian manifolds...
By using probabilistic approaches, Liouville theorems are proved for a class of Riemannian manifolds...
The classical Liouville theorem states that a bounded harmonic function on allofRnmust be constant. ...
Let ℱ be a codimension one foliation on a closed manifold ℳ which admits a transverse dimens...
AbstractIntuitively, a complex Liouvillian function is one that is obtained from complex rational fu...
AbstractIntuitively, a complex Liouvillian function is one that is obtained from complex rational fu...
AbstractFor each n ⩾ 3, we present a family of Riemannian metrics g on Rn such that each Riemannian ...
We prove several Liouville theorems for harmonic maps between certain classes of Riemannian manifold...
In this paper, we prove two Liouville theorems for harmonic maps and apply them to study the topolog...
Let (M,F) be a compact codimension-one foliated manifold whose leaves are equipped with Riemannian m...
Let (M,F) be a compact codimension-one foliated manifold whose leaves are equipped with Riemannian m...
Let (M,F) be a compact codimension-one foliated manifold whose leaves are equipped with Riemannian m...
Let (M,F) be a compact codimension-one foliated manifold whose leaves are equipped with Riemannian m...
AbstractBy using probabilistic approaches, Liouville theorems are proved for a class of Riemannian m...
AbstractBy using probabilistic approaches, Liouville theorems are proved for a class of Riemannian m...
By using probabilistic approaches, Liouville theorems are proved for a class of Riemannian manifolds...
By using probabilistic approaches, Liouville theorems are proved for a class of Riemannian manifolds...
The classical Liouville theorem states that a bounded harmonic function on allofRnmust be constant. ...
Let ℱ be a codimension one foliation on a closed manifold ℳ which admits a transverse dimens...
AbstractIntuitively, a complex Liouvillian function is one that is obtained from complex rational fu...
AbstractIntuitively, a complex Liouvillian function is one that is obtained from complex rational fu...
AbstractFor each n ⩾ 3, we present a family of Riemannian metrics g on Rn such that each Riemannian ...
We prove several Liouville theorems for harmonic maps between certain classes of Riemannian manifold...
In this paper, we prove two Liouville theorems for harmonic maps and apply them to study the topolog...