Add to ORKGLet M be a complete Riemannian manifold and N a complete noncompact Riemannian manifold. Let φ: M → N be a surjective harmonic morphism. We prove that if N ad-mits a subharmonic function with finite Dirichlet integral which is not harmonic, and φ has finite energy, then φ is a constant map. Similarly, if f is a subharmonic function on N which is not harmonic and such that |df | is bounded, and if ∫M |dφ | <∞, then φ is a constant map. We also show that if Nm (m ≥ 3) has at least two ends of infinite vol-ume satisfying the Sobolev inequality or positivity of the first eigenvalue of the Laplacian, then there are no nonconstant surjective harmonic morphisms with finite energy. For p-harmonic morphisms, similar results hold. 1
We investigate p-harmonic maps, p ≥ 2, from a complete non-compact manifold into a non-positively cu...
For Riemannian manifolds M and N, admitting a submersion ϕ with compact fibres, we introduce the pro...
We study polyharmonic ($k$-harmonic) maps between Riemannian manifolds with finite $j$-energies $(j=...
Let M be a complete Riemannian manifold and N a complete noncompact Riemannian manifold. Let φ: M → ...
We will give a criteria for a nonnegative subharmonic function with finite energy on a complete mani...
Abstract. We will give a criteria for a nonnegative subharmonic function with nite energy on a compl...
Abstract. Let M be a complete Riemannian manifold and let N be a Riemannian manifold of nonpositive ...
The theory of harmonic morphisms is one of particularly interesting subclasses of harmonic maps. A h...
We study biharmonic maps between Riemannian manifolds with finite energy and finite bi-energy. We sh...
[[abstract]]Given a complete Riemannian manifold (M, g) with nonnegative sectional curvature outside...
The harmonic morphisms φ : Mn+1 → Nn are studied using the methods of the moving frame and exterior ...
We investigate p-harmonic maps, p ≥ 2, from a complete non-compact manifold into a non-positively cu...
(1.1) A map between Riemannian manifolds is harmonic if the divergence of its differential vanishes....
For Riemannian manifolds $M$ and $N$, admitting a submersive harmonic morphism $\phi$ with compact f...
Abstract. Let N be a complete Riemannian manifold with nonnegative Ricci curvature and let M be a co...
We investigate p-harmonic maps, p ≥ 2, from a complete non-compact manifold into a non-positively cu...
For Riemannian manifolds M and N, admitting a submersion ϕ with compact fibres, we introduce the pro...
We study polyharmonic ($k$-harmonic) maps between Riemannian manifolds with finite $j$-energies $(j=...
Let M be a complete Riemannian manifold and N a complete noncompact Riemannian manifold. Let φ: M → ...
We will give a criteria for a nonnegative subharmonic function with finite energy on a complete mani...
Abstract. We will give a criteria for a nonnegative subharmonic function with nite energy on a compl...
Abstract. Let M be a complete Riemannian manifold and let N be a Riemannian manifold of nonpositive ...
The theory of harmonic morphisms is one of particularly interesting subclasses of harmonic maps. A h...
We study biharmonic maps between Riemannian manifolds with finite energy and finite bi-energy. We sh...
[[abstract]]Given a complete Riemannian manifold (M, g) with nonnegative sectional curvature outside...
The harmonic morphisms φ : Mn+1 → Nn are studied using the methods of the moving frame and exterior ...
We investigate p-harmonic maps, p ≥ 2, from a complete non-compact manifold into a non-positively cu...
(1.1) A map between Riemannian manifolds is harmonic if the divergence of its differential vanishes....
For Riemannian manifolds $M$ and $N$, admitting a submersive harmonic morphism $\phi$ with compact f...
Abstract. Let N be a complete Riemannian manifold with nonnegative Ricci curvature and let M be a co...
We investigate p-harmonic maps, p ≥ 2, from a complete non-compact manifold into a non-positively cu...
For Riemannian manifolds M and N, admitting a submersion ϕ with compact fibres, we introduce the pro...
We study polyharmonic ($k$-harmonic) maps between Riemannian manifolds with finite $j$-energies $(j=...