Harmonic maps between singular spaces I

Harmonic Maps between 3 - Dimensional Hyperbolic Spaces

We prove that a quasiconformal map of the sphere S admits a harmonic quasi-isometric extension to the hyperbolic space H, thus confirming the well known Schoen Conjecture in dimension 3.

Stable Exponentially Harmonic Maps Between Finsler Manifolds

Complete Lifts of Harmonic Maps and Morphisms between Euclidean Spaces

We introduce the complete lifts of maps between (real and complex) Euclidean spaces and study their properties concerning holomorphicity, harmonicity and horizontal weakly conformality. As applications, we are able to use this concept to characterize holomorphic maps φ : C ⊃ U −→ C (Proposition 2.3) and to construct many new examples of harmonic morphisms (Theorem 3.3). Finally we show that the...

Harmonic Maps between 3 - Dimensional Hyperbolic Spaces Vladimir

We prove that a quasiconformal map of the sphere S admits a harmonic quasi-isometric extension to the hyperbolic space H, thus confirming the well known Schoen Conjecture in dimension 3.

Harmonic Maps with Fixed Singular Sets

§ 0. Introduction Here, for a smooth domain Ω in R and a compact smooth Riemannian manifold N we study a space H consisting of all harmonic maps u : Ω → N that have a singular set being a fixed compact subset Z of Ω having finite m− 3 dimensional Minkowski content. This holds if, for example, Z is m− 3 rectifiable [F, 3.2.14]. We define a suitable topology on H using Hölder norms on derivatives...