Harmonic Maps with Prescribed Singularities into Hadamard Manifolds

Stable Exponentially Harmonic Maps Between Finsler Manifolds

On the Dirichlet Problem for Harmonic Maps with Prescribed Singularities

Let (M, g) be a classical Riemannian globally symmetric space of rank one and non-compact type. We prove the existence and uniqueness of solutions to the Dirichlet problem for harmonic maps into (M, g) with prescribed singularities along a closed submanifold of the domain. This generalizes our previous work where such maps into the hyperbolic plane were constructed. This problem, in the case wh...

Harmonic Maps with Prescribed Singularities on Unbounded Domains

The Einstein/Abelian-Yang-Mills Equations reduce in the stationary and axially symmetric case to a harmonic map with prescribed singularities φ : R \Σ → H C into the (k+1)-dimensional complex hyperbolic space. In this paper, we prove the existence and uniqueness of harmonic maps with prescribed singularities φ : R \ Σ → H, where Σ is an unbounded smooth closed submanifold of R of codimension at...

Removability of singularities of harmonic maps into pseudo-riemannian manifolds

We consider harmonic maps into pseudo-Riemannian manifolds. We show the removability of isolated singularities for continuous maps, i.e. that any continuous map from an open subset of R into a pseudoRiemannian manifold which is two times continuously differentiable and harmonic everywhere outside an isolated point is actually smooth harmonic everywhere. Introduction Given n ∈ N and two nonnegat...

Cobordisms of Fold Maps and Maps with Prescribed Number of Cusps

A generic smooth map of a closed 2k-manifold into (3k− 1)-space has a finite number of cusps (Σ-singularities). We determine the possible numbers of cusps of such maps. A fold map is a map with singular set consisting of only fold singularities (Σsingularities). Two fold maps are fold bordant if there are cobordisms between their sourceand target manifolds with a fold map extending the two maps...